I use a spa surface cleaner and one of those plastic scrubby pads, go over the inside of the shell and the jet surfaces, rinse, then drain out that water.
Whatever you chose to use, if anything, just rinse the sides down and drain that water out. When you refill with new water, any amount of residual left should have a very minor impact on your water.
The cleaner I use is a gel made by Baqua Spa/Brilliance (same product different packages), but I'm sure there are other equally good choices out there.
The stuff can even be used with water in the spa- I got turned onto it when I was using Baqua and had to remove that brown ring around the collar junk- the cleaner took it right off.