You would need to make those double-quotes into single-quotes. Double-quotes will interpolate the $() immediately, running basename before find runs. Single-quotes will not interpolate the $(), so the whole string gets passed to find for it to execute each time
It worked when I tried it. Upon investigation, this is because `basename {}` returns `{}`, which is interpolated; thus the exec just uses the full file paths; but as it turns out, `whatis` works fine with those paths.
It won't work with single quotes because `find` won't do that interpolation when it processes the `-exec` arguments; `whatis` ends up receiving a string with a literal dollar sign etc.
I think the kind of interpolation I originally had in mind isn't possible with `find`. Thankfully it apparently isn't needed (at least with my local `whatis`).