I've got plenty of kendamas wet, but they all just dried again fine. Perhaps your "water" had some contaminant in it.
It is unlikely to rot the ken, I'd say. (Trees usually survive rain just fine)
In terms of removing the spot... It really depends on exactly what the splash was. If it was only water, i would expect it to dry out, even if not immediately. If it was something else... Maybe the old "spilt wine" trick of putting a pile of salt or sugar on the spill will draw out the impurity.
Final word: don't worry about it too much!
