Is there an exchange or provider that actually charge zero transaction fee?
Just curious...

Even blockchain charges 0,0001
Like I say - you can use Bitcoin-qt and pay 0.00000000
BTCbut you might risk a very very long transaction confirmation time.
Well, with bitcoin-qt, you can't really send a zero-fee tx unless it is a high-priority one.
You will need to play with raw tx

But, you can create a zero-fee tx very easily with Electrum
