Should I play my records on those cool old radiograms and stereograms?

Definitely not if you care about sound quality and the life of your records!

Radiograms and stereograms aren’t hi-fi equipment. They are furniture pieces that play music, this was their original design intent. They work well for that purpose, but the turntables in these units range from bad to terrible. They use ceramic cartridges that run very high tracking forces and big, fat, conical styli.

This is a recipe for poor sound quality and high record wear, so if you have precious vinyl, get yourself a decent hi-fi turntable with an elliptical stylus, or better. The reduced tracking force and lower in-groove pressure will preserve your records and produce much better sound quality.