You aren’t doing anything fundamentally wrong
Your setup should not cause damage
The antenna doesn’t strictly need ground its specific geometry will only affect efficiency at reception
A quarter wave antenna needs a ground plane to reflect an image so you have a pseudo dipole but when it’s not present stuff still works out okay and you will get many local stations just fine.
Original 6v radio is happy with 5-8 volts and either polarity the radio is good on positive or negative ground because the front end is just a chopper for the power to the ac transformer and it won’t care much at all.
Let us know how it works out
-s