If my right hand is injured can I chant with my left hand?

The initial regulation to chant - or do anything spiritual or clean - with the right hand comes from the fact that the left hand is generally used for unclean things. If you're unable to use your right hand then what can be done? Krishna is no fanatic and He is seated in the heart of everyone. His concern is with the sincerity of the sadhaka (person practicing spiritual life), not the minute details of their practice. So if with sincerity you chant with your left hand, due to a health necessity, Lord Krishna will fully understand.

I hope this is helpful.
sincerely
Laxmimoni dasi