I'd love to have you two on board pun not intended, shyness or not.
While I'm not that shy of a person myself, I know the fear of screwing up and breaking people's expectation. You wouldn't have to worry about that, however, as we'd keep a friendly atmosphere.
Don't want to use the mic? No problem. Made an impossible move? We point it out and explain how to correct it. Don't understand the rules? Just ask.
Actually, because we all like different games, asking about the rules and screwing up from time to time should be the norm, even more so when playing a new game. And even then, screwing up is normal and because everyone you'd be playing with would be 100% fine with it, you wouldn't have to fear it. Playing the top strategies wouldn't be a priority either. Imagine playing a board game with your classmates for the first time. (Or, since I'm a dirty weeb, some sort of a fancy anime school gaming club members)
Hell, if it'd help you, we could start with something simple, or cooperative and move onto other games later. Maybe it'd help with the RL shyness too.