How about Jon Seiger. He sings and plays trumpet, and he's deaf. He also sounds "exactly like Louis Armstrong," as quoted from his band's site. Check out the audio on his site. He does a pretty good job.
One of the best dixieland/traditional jazz tubists I have ever known is deaf for all practical purposes. He has recorded numerous cds with his group and continues to perform regularly. He "hears" by bone induction and feel. Wonderful person too.
This is a topic of which I have some personal knowledge! I wear hearing aids for the purpose of distinguishing the spoken words (think conductor giving directions) but they are not needed for hearing the music and playing dynamically. Louds are not the issue, nor are the softs, but simply the spoken word. So, I,too, often bother others near me trying to figure out what the mumbling conductor just said! It's a pain, but I still hear the music very well, so that's a blessing. Too many years of playing in super-loud bands and then running super-loud power tools in my off hours! I really do recommend that folks wear hearing protection whenever possible!