J.K.
I'm a daycare provider as well, but I put both of my kids in preschool at age 4. For my daughter, who has a similar personality of your son, I wish I had put her in sooner. Kindergarten was hard for her because she didn't have enough experience away from me.
I think that the more you expose him to experiences where he is successful the better. He needs to gain confidence away from you and know that he is ok without you nearby. Many people think it isn't important at this age, but when a child is so shy and anxious about being in a new place (like kindergarten) they are not as able to focus on what they are supposed to be learning. For my daughter, it took a lovely 2nd grade teacher and some maturity to bring her out of her shell.
Also, many kids go through a separation anxiety phase around age 4, so waiting might not help.