OK guys, if anybody else is looking for a solution, I think I have a perfect one.
I used black electrical tape. I attached a length of it to the inside of the lens cap, all the way around the circumference, and then folded it over the lip of the cap and stuck it to the outside too. Standard width electrical tape is a perfect fit, and because it's thin and black and glossy it's virtually invisible. It adds just enough thickness to make the cap a snug fit, and it fits my two requirements of looking professional and being customer-proof.