You will definitely set the fees yourself. No matter what you do on wallets like electrum you are the going to be the one to set your fees.
Once you setup the sweeping private key procedure which includes the recipient address you can go ahead and click on sweep and just like Normal transaction the fees window will open and you can set the fee suitable for you and then proceed to pay or send.
So you're saying after hitting the "sweep" button I can still choose the amount of fee I want to pay?
https://i.imgur.com/w3pz0Kf.pngThat is correct:
Click on sweep and electrum will look up what bitcoins have been sent to the corresponding address. It’ll then display a window where you set the fee and enter the wallet password if any. After you’ve set a suitable fee click on send and the coins will be swept to the address you set in the previous step.
