From Hair Trigger's suggestion about backflip saw, I've got another suggestion.
You know when you are backflipping and you are starting up your minigun or Barrett? The whole startup sound will play, but your gun actually is not fully started up. Then there's chainsaw. When you are backflipping or using the stat gun, the saw sound will play but you can't attack with it at all.
So I suggest instead that if you backflip, any startup or saw sound that is to be played will be paused until the end of the backflip, just like if you are reloading and you backflip. As for saw and stat gun, the sound played when using the stat gun with a chainsaw should also be removed.