You don't need a new computer, just use one that you're certain is clean of malware.  Don't connect it to the internet while you interact with the private keys.  If you don't trust that your computer is free of malware (and even if you do,) the safest way to make absolutely sure is to create a live USB to boot the computer for temporary use.  Tails OS is probably the most user friendly, and safest for the less technically capable.  The advantage with tails is it comes with Electrum pre-installed and ready to receive your private keys.

On an online computer you would use a watch only wallet to create transaction you want to sign, and save it (.psbt) onto a clean USB drive.  On the off-line computer you would import the private key into Electrum, then sign the transaction, and save the the signed transaction (.txn) onto the USB.  Return the USB to the online computer, open the .txn file in Electrum to broadcast the transaction.