The shooting with the non-dominant hand isn't nearly as difficult as proper drawing from a holster with it.
Do you:
a) know how to retrieve your pistol with your non-dominant hand from a holster geared for your dominant hand?
b) know how to properly retrieve your pistol with your non-dominant hand from a holster geared for your non-dominant hand? (do you even have a holster for your non-dominant hand)
I would practice, practice, practice doing either a or b over and over again until it becomes fluid.... then some more. You can also dry fire practice with your non-dominant hand as well. These are things you can do now that cost nothing but your time.
I actually suggest everyone has this in their arsenal of practice regimen. You never know if your dominant hand will ever become injured and rendered useless.
One other caveat... avoid calling it your "weak hand". This sets up a bad psyche about it. It's your non-dominant hand, just like you have a dominant and non-dominant eye.
