You might be asking for trouble if the slots are already cut too sloppy for the thinner hinges. Having said that, I think I would try cutting a piece of 1/64th ply and gluing it into the slot... being careful to get the glue on one side only. If that tightens things up, then I would proceed with the CA hinges and then pin them with a toothpick if still a bit unsure of the tightness of the fit.

Ernie