You don't really have to stand still, you can fidget around. Stand on one leg, switch to the other. Shake a little to the music, etc.. Switch to sitting from time to time. If you're hardcore you can even get a treadmill to go with it.
So in a recent episode of PAX TV they showed one of the penny arcade creators had a gaming system installed in front of a treadmill. Obviously programming's going to be a lot more difficult while walking than playing a video game, so perhaps program the treadmill to move forward a few feet every 30 seconds or so? It might be enough of a small change that you can learn to ignore the small movement while standing and may keep the body from getting stiff.