I think I understand what you are getting at.
Kids may not like something, but won't fight it if for fear of disappointing their parents or getting in trouble. They also feel powerless as parents make the choices for them. Some kids will have tantrums to get their point across. Some kids will sit in a class but will get distracted and will do their own thing t the demise of the teacher. Your son is showing maturity beyond his years as he is expressing his dislike to an activity verbally, without a fuss.
For some reason, parents don't take what their kids say seriously, thus the child gets stressed and goes into tantrum mode. You don't want it to get to this point. Your son may be picking up on the fact that the classes are nearly over, so he is just sticking it out.
Martial Arts isn't about turning a sensitive child into a tough boy. It's about self-discipline and self-defense. It can be repetitive and tedious and loud. Some times just the loudness can make a quiet child intimidated. It's certainly not for everyone.
I'm not sure if you have underlying prejudices to boys that are more sensitive, or if you are just concerned of him being bullied for being sensitive. One of the rules about Martial Arts is to not use it outside of class.
On a positive note, just like with any activity, it can improve his self-confidence. But any activity can do that. Even if you went the opposite direction and put him in dance, if he were to really in enjoy that type of activity, it would be much better on his self-esteem, than to stick with an activity he doesn't really like.
There are so many different types of activities out there for kids. Check out the Leisure Guide (they are free and available in most places where you can get newspapers or other guides to city community services. You can go over all the activities with him. The activities held at community centres usually run for about 4-8 weeks on average, and cost way less. You can try something different every season and sign him up for multiple activities in one season, as long as the schedules don't interfere. If you find there is something he is really enjoying and would like to pursue it further, then you can look into finding a place that offers a more permanent class.
Your son will be fine. Kids can be ever so cruel and they might find anything to pick on him about. But just be carful that your not giving subconscious messages to your son that you think there is something wrong with his personality or give him the impression that he deserves to get picked on for being sensitive. Not saying that you are, but you will be surprised to what young kids pick up on.