I am ambidextrous. I learn't ASL using my left hand even though my dominant hand is my right hand! Why you may ask? Simple! I like to challenge my self and do things I think I am not able to do!
As others have said, either hand is perfectly fine my dear. Simply use one hand signing in a conversation. But, switching hands won't confuse the one your talking to because regardless of what you sign with your left hand or your right hand, the other person is going to understand what you are saying. People aren't that dumb to not articulate what is/being/trying/meaning/meant to be said.
The only ones to be confused if you switch up in conversations are the ones who don't understand/articulate ASL good enough to know what is being signed. Native long time signers, do not get confused, unless your a bad signer.
Explore your possibilities.
