Using mandolin - watery salad.
Interesting. Both fennel and radishes are not particularly "juicy" vegetables, unlike cucumbers or tomatoes. I guess draining would be the way to go, if liquid pools at the bottom of the container. Or salting and draining, in the fashion of cucumber salad or coleslaw, the result, though, being lose of crispness.
Are you sure the "watery" aspect wasn't just your dressing?
That's a new one on me.
This is just a guess: the wording of your post suggests that you put S&P directly on the vegetables rather than into the lemon and oil. That MIGHT have burst the cell walls of the thin slices. I'd suggest you try making the dressing separately before tossing, and see if that makes a difference.