I think you could wax it at home. It's not like the brows where if you make a mistake it's a total disaster - no-one is going to notice that you took off a bit too much moustache on one side and made your mo uneven. You could try the Nads wand because it doesn't need heating or anything and it comes with mo sized strips.

Or you could shave it and use some rogaine on the area to encourage it. One of my friends has a fake moustache and she looks rather dashing