I've done a bunch of screwing around with weird shifters and such and friction works with anything where the indexing isn't controlled by the derailleur (I've never encountered the latter, though I'm sure someone's made one). The only concerns are that the friction shifter can pull enough cable (most likely it does) and your derailleur needs to allow enough travel for your cassette. For instance, if you go from a cassette that's 11-26 or something to 11-36, you'll almost definitely need a longer cage derailleur for the bigger sprocket. If you want to use indexing shifters, they have to index to the same spacing as the cassette requires. You'd have to look it up, but I think the 7- and 8-speed Shimano cassettes have the same spacing, so an 8-speed shifter on a 7-speed rear will work (or a 7-speed on an 8 cassette, but you'll have to not use one of the sprockets), but a 9-speed has the sprockets closer together, so they're not interchangeable. I could be wrong about the specifics of the relative spacing of those cassettes, but the idea is right. A big thing is reducing the friction in the cable housing by using as large radius as possible. I don't know why it isn't more popular, but I prefer to cross-cable where the housing goes from one side of the handlebar across the headtube to the opposite side's housing stop instead of using the cable stop on the same side as its shifter. The cables will cross each other under the down tube, but they'll barely touch and it's a much smoother curve in the housing from the handlebar with the added benefit of less flopping around. Of course, this only works when the cable stops are on the underside of the downtube.
