I make youtube content and I'm trying to find out if it is possible to record the game with the radio on but in post edit that sound out WITHOUT deleting all the other audio with it. Thanks!

Don't see how. When you record gameplay, the audio is all smashed into one track. If you want there to be no radio you'd need to have if off while playing.

If you commentate your videos you can try to talk louder than the radio.

I understand modern music, but will they actually care about 1940s-50s songs?