I'm a massage therapist. It's just you and the client in a quiet room, only background noise is music, which you can turn way down. The only time you have to really talk to them is before you start, when you're face to face to discuss what they need and are what they are looking for in their massage. After that they really don't want to talk. There's forms they fill out before the massage, one has a question "what do you look for in a therapist?" I cannot tell you how many times I've seen "quiet", so its win win for everyone. Sometimes they do want to ask or tell you something during the massage, and it can be a little difficult if you've dimmed the lights real low, but not too bad. Plus there are plenty of visual clues if you are working too deeply and it's making them too uncomfortable. They will tense up the part you're working on, or squeeze their hands into fists or flex their feet.
You won't get rich doing it, but it pays the bills
For a bit there was another deaf therapist working at my spa, he had a cochlear implant.
I should probably warn that to get your license you have to go to school for it, there's the massage therapy classes themselves, in them you have to learn all the major muscles, their attachment points and actions. Plus Anatomy and Physiology, to get in those classes you have to take Biology if you don't have college credits for it already, Public Speaking and Small Business Management.