Like many others have said, not speaking would be interesting, but if you mean the character to be well-developed and relatable, then speaking might be good. If not, then I think not saying anything would be really interesting.

You could always have the character speak, but only a little, or in partial sentences. You could have a person or being who speaks for them, or, if you want to get a little crazy, you could make the character able to project images or ideas into other people's heads or something. I have one character in my unfinished project who will probably have fewer than ten lines in the entire book, so it's possible. She's just a little weird like that.

Like you said, if you choose no talking/extremely minimal talking and still want your character to be relatable, you'll need to prepare to describe gestures, expressions, and nonverbal noises, haha.

Anyway, this sounds like an interesting story! Best of luck with making your choice.