Couple of thoughts:
1) I have seen people use a Euro concealed cabinet hinge. This doesn't require access to the inside while closed, but does demand some careful measuring to install. Also you have to use a forstner bit or something similar to route out a hole for the hinge.
2) If you have an access hole from the back or bottom and can get your hand inside there, you could do a latch type hinge with a cleat. Might be a paid to line it up centered on the CP box, but if you nail some interior strips on the underside is will fit like a deck lid. The latch would then hold it in place.