The club length doesn't matter much if you are a shorter player. Many shorter tour players used standard-sized clubs. However, your swing arc will be on a slightly different swing plane and less vertical than a taller player.
With all the varying heights of players, their golf clubs typically only go from one-half to one inch under or one to two inches over standard-sized clubs.
The key when you hold the club is not to hold the club at the end of the handle. Holding the club at the end of the handle tends to move around and tear your glove.
Your little finger should be about an inch from the end of the club; the cap shouldn't be touching your hand. You will find that you have much more control of the club. It is like having a counterbalance weight on the end of the club.
If you choke down on the club, you won't lose too much distance in your shots, but you will have more control of the club.