US to Canada - VFR, no XPNDR, Light Sport legal

OK, how about some advice on whether this is feasible.

I've got a friend in Canada and I'd like to visit him by
plane. My aircraft is an antique 50 years old, w/o an
electrical system or a transponder. I've got a handheld
radio. The aircraft is light sport aircraft legal. I have a
private ASEL, but have allowed my medical to expire,
figuring I don't need it, so why risk losing the right to
fly by renewing. There's no reason I know of why I'd fail
the medical.

First question is whether I can fly my airplane to Canada
(and it would be nice to fly back too :-) without a
transponder, in view of post 9-11 restrictions. It looks
like I need to be squawking to cross VFR, which I can't do.

Second question is whether I need a medical.

Anything else I need to cross the border if I can jump those
hurdles (such as FCC radio license, passport, etc.)?

Thanks for any tips.