What is a substitute for milk when making ham balls?

As ChrisH said in the comments, probably all that matters is that the milk is a liquid. If the end result is supposed to be something solid, there can't possibly be that much milk in there, and the fat and flavor of the milk are pretty small compared to the meat.

So, just use another liquid. If you're not worried about flavor, water would work. Stock/broth might be a nice small step up. Or if you want to tweak the recipe, you could take the opportunity to add other flavors. There are plenty of flavorful but mostly water things you could try - think of things like worcestershire sauce or soy sauce (though I'm not sure what'd go with your recipe).

If the recipe calls for the milk to be mixed with bread or something else starchy (like this recipe, for example), that's called a panade, and it indeed works with all kinds of liquids.

If you want to closely replicate the water/fat/sugar content of milk, you can use the following (originally from this other question):

• 200 mL water
• 2 tsp pure fat (e.g., cooking oil)
• 1 tbsp sugar

That will produce the equivalent of 1 cup of whole milk. You can substitute the water for some other flavorful liquid (e.g., stock or juice), but you will need to adjust the fat and sugar accordingly.

Note that the bread and milk in the original recipe are used to form a panade: The liquid activates the starch in the bread to form a gel, acting much like a fat to lubricate the protein fibers in the meat and help prevent the meatballs from being hard. Substituting a corn-based product for the bread might not have the same gelling properties. If you require the balls to be gluten free, then I would suggest trying finely milled oats.

My wife and daughter can't do dairy and we regularly substitute almond milk or coconut milk for regular milk in recipes. It almost always works fine. I'd probably go with almond milk for this recipe.

(This is an expansion of my comment -- both more general and more specific)

In many recipes that use milk, the milk is just there as a liquid. Replacing it with a suitably-flavoured liquid is often appropriate (though in the presence of other dairy ingredients be cautious before adding anything too acidic).

You don't give any idea of the quantity but assuming it's small you could try apple juice/cider (a nice pairing with pork if not too sweet). Now when I say cider I mean the alcholic sort ("hard cider"?) -- it's less sweet than cloudy apple juice. If you also want to avoid alcohol, a variation is juice with a few drops of cider vinegar. The flavour is different but can be good with pork. With other meats white wine can work.

In some cases adding (more) beaten egg in place of the milk might work, but some things would become too firm. Given that there's rather a lot of milk in this recipe, replacing it with egg would make change both the texture and the flavour too much.

You could quite possibly use a non-dairy milk (almond/soya/rice) though these won't always substitute for real milk. Again, when they will work is when the milk is being just a liquid. Long, gentle cooking of recipes with milk in often means that non-dairy milks won't work so well. You'd also need to consider whether the flavours work, in particular sweetness.