Hand the party a map
You know this is going to happen: prepare a map of everywhere the imp can go before the session and hand it to the party when they get to the dungeon.
I’ve done this for all sorts of “insider” knowledge: the description from an escaped slave, the blueprints from the architects office and, yes, the exploration by familiar, Arcane Eye and polymorphed PC. It’s quick and easy and it involves all the players.