how much is the fee for sending 0.096 ETH?
You should visit this site
https://ethgasstation.info/That provides a calculator for you to make any calculation about how much the recommended fees to send ethereum. It says standard cost transfer is around $0.009 but i recommend you to put 21k for gas limit and 10-15 gwei and it will cost a little ethereum to pay the network.
I've done several transactions and i use that settings.