So since my btc balance would be the same as my bitcoin cash how would I go about selling the bitcoin if it shows zero balance on my ledger
Honestly every thing i don't understand what are you talking about but base in what i understand what you said here in quoted you wanted to sell your bitcoin cash and if you sold your bitcoin or bitcoin cash it can be turn into zero balance?
It should be turn into balance if you send all of your bitcoin or bitcoin cash to other wallet unless if you are receiving bitcoin or bitcoin cash to other wallet your wallet balance would be increase. .