How can I use white pepper without having the odor dominate the food flavour?

It's interesting that this is your experience, since "common knowledge" is the white pepper is milder than black. White pepper is the dried ripe fruit of the pepper Piper Nigrum, and the black is the unripe, cured and dried fruit. Black is usually hotter than white, but generally they are considered to be interchangeable, with the white being used in sauces and in cream dishes for a better look (no black specks).

Since this pepper is so strong for some reason, I would advise that you only use it in dishes that rely on the pepper flavor to the exclusion of others, say steak au poivre, or pepper pot, or salt and pepper scallops.

Other than that you can cut back on the amount or grind it now and let it sit around for a while...pepper has its strongest, best flavor when freshly ground; it kills me to suggest that, but I'm trying to answer your question.

If it were mine, I would try to figure out a dish that this pepper would truly enhance, as I suggested.

Some people are sensitive to white pepper, which might smell as horse urine or swine manure to them. This is because the fermentation process produces of white pepper produces some of the same chemical compounds. The older the pepper gets the more concentrated the odor will be. There is no way around this if you are one of those who does smell this as it is generally conditioned. You can read this article for more information. https://www.ncbi.nlm.nih.gov/m/pubmed/16028994/

I have loved white pepper on Japanese chicken wings & Thai curry for many years. It is a wonderful spice. BUT, I started tasting it in Thai curry from a particular restaurant a few years ago & was disgusted by the manure flavor. I couldn't make out what part of the dish was tainting my beloved Thai green curry, if my tastes were changing or what. Other Thai restaurants still made it great! Then, I cooked some chicken adding some old white pepper & found that same manure flavor there. Horrified, I smelled the white pepper container, & sure enough it smelled like manure too. So, I purchased a new bottle of white pepper, opened it & took a whiff. The new bottle of white pepper smelled fine (like white pepper is supposed to smell & taste).

So, if you are noticing a manure smell coming from your white pepper, it is not the way it is supposed to smell or taste & it has gone bad or was poorly processed. I've read that if the water is not fresh that bathes the pepper corns before shucking in the making of white pepper, it will have this flavor (Gross!). It may mix ok with a stronger spiced dish, but can taint a dish that relies on the true essence of white pepper (which is definitely NOT the taste/smell of manure). So don't knock white pepper. Knock the guy using old or bad white pepper. Test whiff before use.

I promise you I am not being snarky here: if an ingredient is overpowering the dish, use less of the ingredient.

One cooking site, writes about substitutes for it: "Black pepper is the best substitute, but the differences between the two in both smell and taste are quite distinctive."

Yes, it is certainly distinctive! Using black instead of white pepper may not be bad, but it will simply make a different dish. For instance in mashed potatoes - should I not have white pepper in my house, I'd simply eat something else and not cook mashed potatoes until I have the proper ingredients for it. My mashed potatoes is spotted anyway, from some nutmeg in it. (But those who are only interested in the color and not in the taste can try maize flour instead of pepper, because it will not color it at all.)

Also most types of fish dishes benefit from using white rather than black pepper.