How do you deal with extremely timid/shy students in small classes?
I think stating very clearly that you are available to answer questions (and not just while in class) like office hours or before/after class is important. Some students are more comfortable with email, make sure they know they have your email and that it's ok to use it. Give some positive reinforcement when students ask questions. 

I teach graphic design so I don't have a lot of students (20 at most usually) and a lot of classroom time is dedicated to problem-based learning and most of my teaching is coaching. I go see every student to check how they're doing and ask if they have any questions. It's difficult for them to get their work criticized in front of everyone at first so I'll do small group meetings instead of whole class presentations. 

I think most shy people can open up when they're around people they trust so I think establishing trust with the student as a teacher is crucial. You can make them work in small teams so they get to know each other better and build up slowly from there. 

I don't think it's something you can fix in a single course so there is only so much you can do without affecting the whole classroom.