You could transfer some BTC to a blockchain.info wallet and then use the "Shared Send" function. 0.5% transaction fee
https://blockchain.info/wallet/send-shared
https://blockchain.info/wallet/send-shared
Blockchain.info Shared Send is no longer recommended. Shared Sends leave an easily tracked pattern in the blockchain.
State of the art at present is to use Monero. Buy Monero with bitcoin at one exchange than after time has passed sell for bitcoin at a different exchange. Use a local Monero wallet, not a web wallet for maximum privacy.