That's fucking incredible and it shows that Joker is primarily concerned with accomplishing the dumbest tricks possible. And before you say "Oh, he might have had it around for another gag," remember that this Joker already created a joy buzzer that roasts you alive when you shake his hand. He's out to kill. He's not going to leave it in some other mob boss' grip and walk away. No, the Joker, before he even decided to throw his big, Prince-fueled poison gas event, decided that he needed to be ready just in case someone was hanging off the side of the very high place in front of him.
"Hold on. Just wait there for a second. I have just the best thing ever to show you."
He carried around a fake hand for at least a few hours, hoping to eventually run into someone that needed help pulling themselves onto a roof. And I'm not so convinced that Batman was always meant to be that someone. If Joker had been dancing on his float and saw someone dangling from a nearby skyscraper, he probably would've stopped the whole thing. "CUT THE MUSIC. CUT THE MUSIC. TURN THIS SHIT OFF. I GOTTA GO USE MY HAND."
That is such a magnificent waste of time and manpower and pocket space. Joker created a pistol that could shoot down a plane invented by the smartest crimefighter in the universe. He had the resources and know-how to create a whole murder parade that everyone in Gotham, except Alfred, went to. If he had not been such a painfully terrible troll, he probably could've invented an anti-Batman towel or something. But whether it was a spur of the moment decision or a fetish that he'd wanted to act out for years, Joker created a dummy hand just so he could prank a person into falling to their deaths.