How do you deal with the students who have an opinion, but are worried about what the other students might say or think?

Just give them a chance to talk.

I 'prune'them,pretend they aren't there and move on with the rest of the group.l have seen this method to be not only effective but a good antidote for such characters.

Remove the fear in them tell them all are not perfect.Everybody learns through failure.Giving them the confidence that even the teacher himself or herself learns everyday.Everybody makes mistakes and learns fromthat mistake will surely help them.

Ig i am a teacher , the first think i MUST teach my students is never affraid of saying the information you know , as you always have2 choose eiher its correct then you will be a winner but if you didn't say it then you are double looser by loose first the chance of may be you win and second if false at least you give yourself the chance to say it which mean you make effort to think , which think is the first step of succsess, as know one born with information but we all gain it by knowledge and by thinking first.