Bitcoin exchange where you can set your own wallet instead of using one provided by the exchange
You forget something. Who pays it then?


  I basically want to avoid the extra cost of transferring...  


That means that the people of the exchange have to transfer it for you and that means that they have to pay the fees because it's a default blockchain transaction and the miners want to be paid. And the exchange's owner does generally not want to donate you 20-30$ (average fees at the moment)

I don't think that there is such a platform you are talking about. Exchanges don't work this way