For this soft side cooler, the self-adhesive velcro should work fine. It's not like he is going to be taking the patch off a lot so there is minimal abuse to the adhesion. And if the patch needs to come off; as long as he has hold on the lower velcro piece, he can pull the patch off without an issue.
I know this because I have several patches on my tactical gear, and a couple are attached this way, and I have yet to have one peel off.