SRAM, Shimano, and Suntour 7 speed cassettes all have 5.0mm center to center gear spacing so it should work. Personally I would not go to twist grip shifters as in my experience they may work when new but soon they all work poorly and are much harder to maintain than other types of shifters. They typically only come on lower end bikes.
Just my opinion, but I fix up a lot of cheaper donated bikes for a couple local charities and I have seen many twist grip shifter thrown in the garbage.