I'm not even sure you would need to exchange it to another coin. You would never be exchanging it to USD because USD withdrawals will require you to identify yourself and a corresponding bank account. To withdraw crypto you just need an address.

So you can exchange it to BTC or ETH and withdraw. Or you can just deposit it and withdraw it after. Most exchanges just mix customer funds together, so as long as the exchange has enough BTG balance minus the double spent deposit, they will send you real BTG.