Right click check

I'm trying to do that with command blocks, but could switch to datapacks if needed.
I'm using a scoreboard to store if player right clicked with a carrot on a stick, but the problem is: player can't be holding a carrot on a stick all the time, so I want to set it in the player's offhand, and set back to whatever item the player was using before, is there a way to do that?
My English is not that good, sorry. If needed I can explain better i guess