Well, as I pointed out earlier, the location of Radagasts' residence was hardly conducive to regular washes. I don't recall even in the movie a slight glimpse of a stream, etc, unless I missed it.
Nor Toklein addressing these kinds of lifestyle issues. He focused on the story events and themes, not these lifestyle decisions
. So it relatively a speculative issue. Did he CHOOSE to leave that poop on his face, or have difficulty regularly washing?