Use compressed air. One of those portable 12 V compressers you can carry in your trunk to refill a flat tire should work. Use the fitting supplied with the compressor for filling air mattresses and jam that into the drain hole, then wipe a mixture of dish soap and water around all of the seams and fastener locations and see where the bubbles come out. I have read you can actually do this on bigger boats using a shop vac with the hose on the outlet side to pump air into the cabin (after sealing as much as you can with duct tape). Let us know how it works out.
Catalina 38, Hull #112
Grosse Ile, Michigan