Going by logic (no definitive knowledge here) I would think that power would affect slingbow as it generally increases damage to creatures and blocks. However, I can’t really see how swing speed would correspond to a slingbow as firing speed isn’t really the same thing.
I do have a bit of knowledge in this as I have focused on a sniper themed build for hunting.
From my experience the stats which effect the slingbow are Power, +%50 damage at max and Agility +%20 critical chance at max. Sadly neither Dexterity or Control seem to affect it.