As a parent i understand your worries about your kid but i think you should meet his teacher.First ask your kid why he feel so shy.May be his classmates makes fun of other kids who are using toilets or he dont like using school toilets.At this stage we cant be rude to kids so ask him politely if there is any other issue.Tell him what can happened if he is not going toilets at time.Make some story and tell him.Hope you will solve this problem as soon as possible.Please let us know also.
My daughter had similar problem. When we inquire in the school regarding the same, they agreed that one of the care taker(AAYA) from the school scolded her while my daughter was using the toilet. From that incident she used to avoid using toilet. But gradually she forgot about the incident and now use school toilet. So ask your kid if the same has happened with him in the past.