In electrum wallet do I need to subtract the Bitcoin mining fee manually, or I can send all my bitcoins in the wallet to shapeshift/exchangelly?

You just send Bitcoin with sufficient fee in a same way that you send Bitcoin to a standard address.

Here is the quick way to exchange BTC for ETH at Shapeshift.io
1. Paste your Bitcoin and Ethereum addresses in the filed below

2. Send some Bitcoins that you want to exchange to the address where shapeshift gives. It depends on how fast you want to get the transaction done. If you want to get it done in 10 mins, you probably have to pay approximately 500 satoshis/byte for the mining fee.