Following the KISS principle I just leave the handle on the ice cream bucket and use a longish bungee to go up to the other end of the drill. Cheap and easy, which is usually a good thing, except in relationships ;-). The buckets will eventually deteriorate where the blades rub but you will just have to buy more ice cream. I recommend Burnt Almond Fudge, the cheap kind at Macey's. If you lose the bungee in the snow while out fishing, the bucket stays on fairly well without it. And it never hurts to take a spare bungee on your sled anyway. Or you might get one from a companion (thanks 2knots). If I were you I would try this and see if it works for you before laying out more money for a boughten one.
The older I get the more I would rather be considered a good man than a good fisherman.