Interactive Brokers for large amounts and even for smaller amounts (sub $25K) lets you make the physical currency trade at the spot market rates the banks get, and withdraw the proceeds in most major currencies including AUD, CAD, CHF, CNH, CZK, DKK, EUR, GBP, HKD, HUF, ILS, JPY, MXN, NOK, NZD, RUB, SEK, SGD or USD. In addition, IB-India accounts are required to maintain a Base Currency of INR."
This said, if all you ever do is exchange currencies and withdraw proceeds, in my experience IB will eventually close your account. They charge tiny $2 commission on forex regardless of the size of the trade and the AML
KYC isn't worth their trouble if you aren't generating some revenue.