CoinPayments API should do the job. I believe they only charge a fee (0.50%) when you're accepting payments but not for withdrawals.
They charge fees on transfer of funds too.
On-chain transfers i.e. withdrawal to personal address is done free and they only charge network fees (which is high as well, for example, they charge 12 DOGE per transaction for Dogecoin which is 6 times the average dogecoin fees on other wallets).
Off-chain transfers are done @ 0.50% (this is what I think OP is looking for).
Fees details:
https://www.coinpayments.net/help-fees