Because you do not have the private key to that wallet, you can not recover the coin, but the coin is with the exchange B that do not support it, contact exchange B support care for your coin recovery.
That is the only what you can do as you do not have the private key to the address you sent it to, the exchange B has it.
I agree, that's your only chance!
You have to hope that the exchange will pay you back the coins. Because only it has the private key to access the coins on the other chain. If the exchange has not implemented the other chain, then they will most likely not bother to implement it just to give you your coins back. This is your only option, although I think the chance of success is rather low.