Should not be a great problem
They will physically interchange OK
Wiring will be a problem if the Cub was fitted with a Briggs you will have to make up some new plugs to join the wires together.
Another other problem is the alternator output.
Mowers with manual PTO's usually have small capacity alternators which will not generate enough power to run the clutch and charge the battery which will eventually run flat.
I have a quite a few customers with mowers like this and are happy to only mow 1/2 their lawns then pop the mower back on the charger rather than pay for a bigger alternator.
Carbies are the last real problem.
Mowers have 3 types of fuel delivery
1) gravity
2) impulse pump
3) electric pump
The carb originally fitted to a mower is set up for whatever type of fuel delivery so when ou swap the engines , swap the carb with it.