Should old electronics be polarized?
If equipment, whether old or not, has a unpolarized plug, leave it that way.  In fact, don't mess with anything related to that.  Each piece of equipment was designed a particular way.  You don't know all the design criteria that went into it, tradeoffs made, and possibly parts of the unit relying on it being as designed.  Leave it alone, whether polarized or not, old or new, 3 prong or 2 prong.

This is especially true if you let others use something you have modified.  If they get hurt from it electrically in any way, the blame will be on you.  This has nothing to do with whether your modification was the cause or not.  If I was on the jury, I'd probably not believe you did only what you say you did.  Now imagine how a lawyer would hype this to people who don't know anything about electricity.  You open it, you own the liability.