Not an option for most, but some of my friends (and myself) have done front squats with just the bar resting on the delts/chest and the elbows raised high and arms (around 90 degrees) raised in front. Bar just cradles onto the delts, not really going anywhere. So any grip is not needed when actually squatting.
Also done front squats with the bar hooked, or cradled, in the bend of the arms. More of a power lift than anything else. Take the bar from the floor or supports.......either way. Don't recommend this movement for the average trainee, advanced or not, but nice to try now and than..
Far as the grip goes, even with the bar on the finger tips, may have a slight carpal tunnel problem. Which, again, relates to nerve blockage. Could try regular hands flat on the ground push ups, as a warmup for the wrist, before front squats. Palm/hand stretches against a wall (also elbow stretches against a wall, door way, etc) There are also martial arts hand flex exercises for the wrist/hands. If you need straps, some very good suggestion by other guys here.
When racking the bar, a feeling of tightness and a jarring comes, suggest a lat/spine flexibility issue. Could apply to the wrist too. Try keeping the wrist warm also.
Good Luck.