Could I use chili powder in a homemade hot sauce recipe?

Sure, you can do that. It'll be a slightly different style of hot sauce than you'd get with fresh green chilis, less bright and fresh pepper flavor, more of a deep, rich flavor. If it's just a plain pepper and vinegar hot sauce, with the peppers providing a lot of the bulk, the texture isn't going to be the same, though.

If the lack of that brighter pepper flavor is an issue, you might seek out recipes that already have plenty of non-pepper ingredients. Acids like lime and vinegar, fruits, and herbs could all help fill in the gaps.

Also, I don't know how severe your boyfriend's allergy is, but if you end up experimenting a lot, I'd suggest being careful to have him try chili powders before you use them in large quantities. I've never heard of chilis being peeled before made into powder, so I wouldn't be too surprised if not all chili powder is actually okay for him.