Radish greens are peppery tasting, like arugula, and they are much less delicate than arugula. Those two factors probably decide whether you want to use them in salad.
As for their perishability, the sooner the radishes and the greens are separated, the better. I bought some big, fresh bunches of radishes on Monday and I was determined not to let them go to waste, so I used them in a skillet dish that also included butternut squash and canned black beans. Didn't get it exactly right the first time but there's plenty of time for experimentation.