There is a somewhat detailed answer to that question.
a) Do you know what voltage is needed to keep the memory function in operation?
b) Given that a battery is the mother of all capacitors, just a bit slower as a chemical engine, you should be able to do a proof-of-concept.
c) And once you have determined the operating voltage (somewhere between 1.2 and 3.5 VDC at a guess), you will have several choices, including your diode option. BUT:

Caveat: Batteries do not like seeing a dead/partial short. So when diode you install is not in use and the circuit is OFF, the battery is in parallel with whatever device is in place, whether a super-cap or a button cell, or something else. If that is shorted, so is the battery. OOPS! It really does behoove you to find the OEM source and repair/replace it as designed. You do not want to wake up one morning and find that your installed battery has spilled its guts all over everything.

Remember the Revox B760 tuner? It had two AA cells under the fold-down door on top of the faceplate. Trust the Swiss to take the very simple brute-force approach.

Peter Wieck
Melrose Park, PA