A mediocre Base 50 Power HM move has saved you? On MANY occasions? You must have one damn good Furret, hahaha.
I suppose if you really like an attack on it, I won't recommend a change. cough RETURN OR SLAM. cough*
Amnesia isn't necessary, but if you want to keep it, it won't be a bad thing. If you are looking to changing it, I would replace it with a coverage against Rock-types, like Dig, Brick Break, or Iron Tail.
Sucker Punch is a great idea on a Pokemon on Furret. Although in-game, it can take a bit of prediction, due to the random attack choices from typical trainers and their stupid AI. Still, it gives priority and coverage against Ghosts, so kudos!
Finally, Charm is a great idea on Furret. A sharp Attack reduction is extremely useful on these typical Field-bound Normal-types.
All in all, this is a pretty awesome moveset for Furret. It gives a combination of power and protection, which should be the strategy on every Normal-type Pokemon.