You can use the RD.

The shifter, however, perhaps. 7 and 8 speed shifters don't pull the same ammount of cable. They can be mixed, but not all the gears will work perfectly. They'll usually work well enough for most people, but not perfect.

So I'd use the RD, but keep the old shifter, changing cables, housing and tuning it properly (RD limit screws and B screw for start). Check the chain length, if it's too long, that can affect shifting.

Shifter compatibility with cable pull and things to pay attention to:
7) Bicycle rear shifter compatibility - Cycle Gremlin

Chain length sizing:
Chain length sizing for bicycles with derailleurs