In white "chocolate" fudge the white chocolate adds fat, from cocoa butter, sugar and vanilla. White chocolate is mostly about texture and has little flavor of its own. In my opinion white chocolate isn't particularly useful in white fudge because the cocoa butter doesn't enhance the texture much and the sugar and vanilla are more easily (and inexpensively) added separately. In regular, chocolate, fudge there is no cocoa butter and the cocoa powder is used purely for the flavor.

Fudge is a creamy candy. It is creamy, and reminds us to some degree of chocolate, because of the small sugar crystals. The cocoa powder in chocolate fudge doesn't play a significant role in the texture of the candy.

You can leave the cocoa powder out of your chocolate fudge recipe and use other flavorings.

As ChrisH wrote in a comment, it might be easier to simply start with a blank-slate fudge recipe that has no cocoa powder. It will likely be very similar.

As noted by ChrisH in a comment and further discussed in Sobachatina's answer, chocolate is not a necessary ingredient for fudge. If you do not mind a higher-fat recipe, consider using a recipe like the BBC recipe referenced by ChrisH, replacing the butter with one of the suggestions in the Replacing Butter section of this answer.

Executive Summary

If your primary goal is eliminating flavors contributed by white chocolate, the best replacement for white chocolate in your white chocolate fudge recipe is refined coconut oil. This may produce a softer end result.

Start from the white chocolate fudge recipe and replace the white chocolate with refined coconut oil and sugar. The additional sugar can be added with the rest of the sugar, and the coconut oil can be added with the butter.

New ingredient list with butter:

• 2 and 1/4 cups white sugar
• 1 cup milk
• 2 tbsp butter
• 2 tbsp refined coconut oil

If you want to further reduce the butter flavors in the fudge, replace butter with refined coconut oil.

New ingredient list without butter:

• 2 and 1/4 cups white sugar
• 1 cup milk
• 4 tbsp refined coconut oil

White Chocolate Properties

White chocolate contains

• Cocoa Butter
• Sugar
• Milk Solids
• Vanilla and/or vanilla flavors
• Emulsifiers

There are a range of possible proportions of ingredients in white chocolate. However, assuming that you are in the United States, there are legal regulations restricting the proportions of some of these ingredients.

Notable FDA requirements:

• not less than 20 percent by weight of cacao fat

• not less than 14 percent by weight of total milk solids

• not more than 55 percent by weight nutritive carbohydrate sweetener

• not less than 3.5 percent by weight of milkfat

The following derivation of the proportions of ingredients in white chocolate uses the nutrition data of a Ghirardelli White Chocolate Baking Bar (Chosen because, anecdotally, it appears to be relatively common in grocery stores on the West coast of the US).

According to the "per 100g" column in the linked source, a Ghirardelli White Chocolate Baking Bar consists of

• 33.33% (1/3) fat
• 6.67% (1/15) protein
• 60% sugar

Further derivation assumes that all protein is from nonfat milk powder (listed as an ingredient for the white chocolate bar), and uses proportions from the same database.

• 3.16% water
• 36.16% protein
• 0.77% fat
• 51.98% sugars

If ignoring water, fat, and mineral content, nonfat dry milk consists of 41% protein and 59% carbohydrates. Plugging this in to the white chocolate ratios produces

• 33.33% (1/3) fat
• 6.67% protein from milk powder
• 9.6% sugars from milk powder
• 51.4% other sugars

or

• 33% fat, mostly cocoa butter with some milkfat
  • At least 3.5% milkfat
  • The rest of the fat is cocoa butter (up to 29.5% of the entire bar)
• 16% nonfat milk powder
• 51% sugar
• Small amounts of lecithin and vanilla

These proportions (1/3 fat, with the rest being mostly sugar) is assumed in the rest of this answer.

White Chocolate's Role in the White Chocolate Fudge Recipe

Adding white chocolate will add cocoa butter, sugar, milk solids, and vanilla to the fudge. The fat, sugar, and milk solids contribute to the fudge's texture, while the vanilla and milk solids contribute to the flavor.

As noted in this white chocolate review by Serious Eats,

Almost all white chocolate is made from deodorized cocoa butter; that is, cocoa butter that's filtered and purified to make it a more neutral base for cosmetics.

This means that cocoa butter's contribution to the flavor and aroma of the final product is relatively subtle. Vanilla or vanilla flavoring may be the strongest contribution to the overall flavor, followed by milk solids.

Given that the recipe with cocoa powder adds another 1 ounce of butter, it is likely that the fat is significant to the structure of the fudge in the white chocolate recipe.

The sugar and milk solids in the white chocolate is used instead of the cocoa powder in the white chocolate recipe. By the ratios calculated earlier in this answer, the 3 ounces of white chocolate contain about 43g sugar and 13g nonfat milk powder. The milk solids are equivalent about 2/3 cups of nonfat milk.

For simplicity, I recommend replacing the milk solids with more sugar for a clean 1 part fat to 2 parts sugar replacement of the white chocolate. This will also further reduce the contribution of milk to the flavor of the fudge. If you have nonfat milk powder on hand, you can attempt a ratio of 1 part nonfat milk powder to 2 parts fat to 3 parts sugar.

Possible Replacements for White Chocolate

For both replacements discussed here, the suggested replacement is

2 oz sugar (About 1/4 cup by volume) and 1 oz fat

as a replacement for 3 oz white chocolate.

Refined Coconut Oil and Sugar

Refined coconut oil is relatively flavorless (similar to neutral oils like canola) and is solid at room temperature. Its texture is closer to butter's texture than cocoa butter's.

If you want to add coconut flavors to a recipe, virgin coconut oil can also be used. It has a texture more or less identical to that of refined coconut oil, but retains a subtle coconut flavor.

Deodorized Cocoa Butter and Sugar

This option may be overkill for this recipe, but you can attempt to closely replicate the texture of white chocolate by using cocoa butter, which likely accounts for the majority of the fat content in the replaced white chocolate.

The cocoa butter must be deodorized; otherwise, it will contribute a significant chocolate flavor. I note this from personal experience tasting white chocolates made with deodorized and non-deodorized cocoa butter side-by-side. Slightly less anecdotally, Serious Eats notes the difference in their review. Relevant quote:

El Rey is one of the few chocolate makers to use less refined undeodorized cocoa butter in their white chocolate, and to some (though notably not all) of our tasters, the cacao pod's wild flavor does come through loud and clear.

Note that deodorized cocoa butter that is not food-grade is used for cosmetics, so be sure to get food-grade cocoa butter if using this option.

Fudge-Specific Considerations

Replacing Butter

most of my family dislikes the buttery aftertaste most 'traditional' fudge has

As noted by ChrisH, and you in your comment, there exist fudge recipes with a higher proportion of fat to sugar. If it is specifically the taste of butter and not the mouthfeel of a higher fat content that your family dislikes, I recommend a 1:1 replacement of butter by one of the described alternatives by weight. Refined coconut oil, my top recommendation, is also close enough in density to butter for a 1:1 replacement by volume to work.

The simplest replacement is replacing each tablespoon of butter with 1 tablespoon of refined coconut oil.

Aside: More general butter replacement

In the United States, butter will have at least 80% milkfat. The rest is primarily water, with some protein and sugars. In many recipes which include sugars and proteins from other sources, I was able to ignore the protein and sugars, and use a 5 to 1 refined coconut oil to water ratio (by weight). I have tested this in caramels, brownies, and pie crust, though I have not tested this substitution with fudge specifically.

For two tablespoons (one ounce) of butter, this means about 23 grams of coconut oil and 5 grams of water. If you do not have a kitchen scale, 22.5 mL (1.5 tablespoons) of coconut oil and 5mL (1 teaspoon) of water is probably close enough of an approximation.