You can't spend, transact any Bitcoins while you are offline, the easiest way after Electrum sweep and or import is by trying
blockchain.info import your address as watch only and when you click on send or spend it will ask you for private key.
Stop being paranoia and trust me when I tell you, no body is ought to get your coins that easy.
Now tell me how many BTC you have BTW? I could pick some of them from your shoulders if you feel burdened. lol
Entering your private key into an online computer kind of defeats the whole purpose of cold storage. The best way is to sign a transaction using an offline computer, copy the signed message and then broadcast it.
It is best to be paranoid while dealing with bitcoins.