Keep in mind that sweeping and importing are two differet things.
Sweeping means to send the coins from one address to one from your wallet. When you choose the 'sweep'-function your wallet automatically creates
a transaction from your imported private key to an (unused) address generated by your wallet. This costs transaction fees.
Importing simply means to import a private key into a wallet. This does not cost any transaction fees since no TX is being created.
But please keep in mind that this imported priv key won't be included in your old backups, your seedphrase, and not always in a new backup (depending on backup-type and wallet).