The mouth piece is the way to go. However, you do not have to spar with others. You can train footwork, the bag, jump rope, etc. Then when you are ready, you can spar, when and if you want to. Just a thought.
A great way to prevent damage to your inner lips are by getting yourself a mouth piece (consider a size larger cause of the cause of the braces) then boil the mouth piece and shape it into your teeth.
Thanks! Your answer is awaiting moderation.