https://coinranking.com/coin/bitcoindiamond-bcd/exchanges?order=price
I'm sure you've used binance and kucoin already but the 2BTC limit for non-verified replenishes every day (you can check it on their site it's the limit per 24H) but the risky part is we don't know when will the "your account showed suspicious activity pls verify your acc" card will show up. It tends to show up on big amounts tho as it is noticeable so tone down the amount you trade each day.
Binance is perfectly fine for that. I doubt OP is a mega whale trying to unload his coins where Binance's 2BTC/24H withdrawal limit forms an obstacle.
For every 1BTC you held before the fork, you have 10BCD after the fork. BCD currently trades at a value of $1.31 or 0.000115BTC. He can cash out 13,333BCD per day on Binance.