In the most games I saw list of skills the one can apply usually differs from the complete list of skills. Say, in Fallout you don't have even a way to apply gambling or small guns. In Dwarf Fortress you don't have a way to apply, say, swimming. In Cataclysm DDA there is separate last of possible actions which has actions grayed out as long as you can't apply them due to any reason. Skills are separate lists everywhere there... Can throw more samples if needed.
Hence I would filter out all the skills that cannot be applied at all from apply skill menu. But would retain a way to see them in tab near character info and obviously during level up. I'm not 100% sure why but don't think many existing players would like the idea. Probably because of changing the habit.
Secondly, if you integrate manual into the game and make I go about skills appear as tooltips and add viable alternative for keyboard / ASCII (e.g. '?' followed by a latter) many questions about why some skills are inapplicable in some contexts or inapplicable at all would be sorted.
The last thing, but probably not an excuse, some players do like messages game gives when trying to apply skill while impossible