i always thought you would apply kotegaishi on the hand holding the weapon. and something else like ikkyo/sankyo if it isn't and the other hand is.
maybe i'm wrong, but i learned the rolling one from my first dojo - a ki society splinter group... ie tohei lineage. My current dojo does the what i presume you call kotegaishi nage type. The way we are suppose to do it, uke has no balance to launch a powerful strike before having his face splatted ont he ground.... but with a sharp weapon he will have a chance to cut us.