Rans Enduro Sport, Hase Kettweisel Tandem, Merin Bear Valley beater bike
I agree with Hillrider.
I've tried mixing and matching various combinations of 7-speed and 8-speed components for years. The actual cog spacing is very close and, in index mode, I can get it to kind of work (just shift past the last shifter detent to the derailleur limit stop).
There are folks who claim they can get the shifting to index perfectly but I'm not one of them. They are either better bike mechanics than me or they're less picky than me. If it was my bike I'd try for a while to get it to index and convert it to friction if I couldn't.
Just today I put 105 7 speed DT shifters on a bike with an 8 speed cassette and got it to work smoothly in index mode. Since rx100 is supposedly the same as 105 with a different finish, you should be able to make it work. 7 and 8 speed spacing is nearly the same, they only added 4mm to the freehub body to accept one more cog. The only issue is that the drivetrain will be very sensitive to cable tension. It took a little barrle adjuster fiddling, but it works fine.
Also, you would have to lose one of the other cogs instead of the 11t lockring cog if you wanted to go down to 7. I rode an 12-23 8 speed cassette minus one cog on a 7 speed system w/o any problems, but I chose to drop the lagest cog. You will have to run such a cassette "loose" or get 7 speed pins that lock the cassette together. I wound up filing down the pin on my Sram 8 speed cassette in order to run it as a "solid" 7 speed. Hope this is helpful.