How long have you been playing, what level are you currently at, and what pieces are you working on? Also, you want to improve agility, accuracy and speed in your left hand regarding what? (octaves, scales, trills, etc? - or all of the above?)
It makes no sense to say you should play Chopin-Godowsky, Czerny, Hanon, or anything else if we don't know what else you've played - or even, if you have already been beating yourself over the head with the above. For example, you may not yet be advanced enough to play Chopin-Godowski etudes, you could do more harm (through injury) than good by working on them.
There are a variety of things to consider:
1) Most importantly, what has your teacher suggested. He/she knows your playing - strengths and weaknesses - better than we do.
2) It's not so much what you play as how you play it. A suggestion to play Hanon or Czerny is useless on its own. The way you should practise is hands sepatate, in rhythms, relaxed elbow and wrist, making sure you use your torso, shoulder, upper arm, forearm, wrist and fingers in a coordinated fashion. Also, observe your right hand, arm, etc, assuming they are more agile, fast, and accurate than your left. What makes your right hand "better" than your left? Have your right hand teach your left hand.
3) Scales and arpeggios are also useful for developing the left hand, if you apply #2 above. When you become more advanced, you should think about developing technique with the pieces you play. Isolated technical problems can be addressed with specific etudes or exercises.
Topic: Methods to improve hands and fingers