Very interesting question!
Given that you don't know what to do with the checked exception means that the checked exception probably shouldn't be checked in the first place (e.g. SQLException, IOException, etc.). The common approach here is to wrap it in a runtime exception (for SQLException, I suggest jOOQ's DataAccessException).
A bit less common is to "sneaky throw" the checked exception again:
You could also use jOOλ's Unchecked for this, possibly:
If you know you need to catch the specific checked exception somewhere outside of that mapper, then you'll have to be creative. But chances are high, you don't.
I hope this helps,
Lukas