I have some btc in a cold storage made several months ago with electrum 1.9.8, it's on an old pc used only for this purpose.
Should I transfer the bitcoin to a new wallet created with 2.3 or can I let them sleep there for some more months/years?
If its working as it should, I would not update. 1.9.8 is heavily tested and used. Its pretty reasonable to assume that most bugs and quirks have been found and fixed, esp. any major ones. Any internet related vulnerabilites do not effect you, so you do not need the latest version anyway. If at all I would consider switching once Electrum 2.x is more mature.