Those little transistor amps have a very special sound - here's a quick Wiki to bring you up to speed:
https://en.wikipedia.org/wiki/Deacy_Amp
In my experience many of the 'less expensive' practice amps out there sound awful. The amp is part of the instrument; a guitar is about having fun and I fully understand why the OP would want to use an old radio... It's fun!
The high impedance input will be OK and guitars have more output level than you might expect.
Here's a handy little piece of research giving guitar output levels and impedance info that should help you.
http://tomsguitarprojects.blogspot.c...ge-levels.html
Get in there and create something! Make your own sound like Brian May and John Deacon did
Cheers,
Steve.