Seems like this thread came up once before. Yes, you can rechamber a 310 cadet to .32 WS, but it's a BAD IDEA.
Look at the outside barrel dimensions and measure a .32 WS case (30-30 will do as well) near the base of the cartridge case. Seems to me that the chamber walls are going to be might darn thin at that point. I sure as God made little green peanuts wouldn't was somewhere between 30K and 40K PSI anywhere near my ugly puss with chamber walls that thin.
Yes, It can be done. Whem 310 martinis were cheap way back when, I bought one in .32WS. I never had the guts to shoot it, because when my gunsmith looked at it, he felt the gun was dangerous. He gave me in trade what I paid for it to get the action for a pet project.
You could do it and shoot light cast bullet loads, but in that case, just rechamber it to 32-20 and use a proper sized cast bullet. In fact, if I ever come across another one that's original, that's how I would go about it.
FWIW, in 1957, original unalthered 310s sold for $9.95, converted to 32-20, $15.95, .32WS, $20.95, and for the big spenders, in .38 Spl. .357 Mag., $35.95.
Would love to find a few at thoses prices today.
Paul B.