There are other ways to split the coins. The simplest one would probably be to send a small amount of BCH to the address (which only exists on that chain), wait

There are other ways to split the coins. The simplest one would probably be to send a small amount of BCH to the address (which only exists on that chain), wait for it to confirm, and then move all the coins including the BCH making the transaction only valid on that chain. You can then do the same on the BSV chain, leaving the BTC chain untouched.