Newbie here. I am looking for an online wallet that will support me to import Bitcoin paper wallets, then sweep each one to a new paper wallet, at the lowest fee. I had a few accounts from three years ago and finally acted on getting my modest Bitcoin on paper wallets. After much research I chose paper, printer, method and BitCoinPaperWallet to generate the keys. A few days ago I read on Coindesk.com that there have been many reports of people losing large amounts of Bitcoin due to a probable back door problem with BitCoinPaperwallets servers. I do not have large amounts, but still want to be cautious. So, I want to move my several paper wallets to ones generated by BitAddress.org. I want to import the wallet to an online wallet and then sweep each one to my replacement wallet. My logic is that importing can be done without miner fees. With Bitcoin miner fees being upwards of $20 and taking 8 hours at that, at least using the import function would cut fees and time in half. I signed up with Trust Wallet, owned by Binance and after many hours and finally submitting a question was informed that they do not support importing Bitcoin wallets. They do support importing Etherium and many others. Odd. Can anyone recommend an online android smartphone app for me?
If you simply import your paper wallet's private key to another wallet, then you will not be protected against the backdoor that is being used to steal funds stored on paper wallets created with the code you mentioned. This is because importing the key will not move the BTC to a new address, it will simply allow the new wallet to spend the coins that are stored at the paper wallet address. Nothing would stop the thief from also being able to move those coins.
To protect yourself, you need to move the BTC to a new address, which was generated using secure software/hardware.
I would strongly recommend against using a web-wallet. Instead, I would recommend starting here: https://bitcoin.org/en/choose-your-wallet
My logic is that importing can be done without miner fees
Depends what is happening. Are you importing or sweeping? Importing means the wallet is just saving the private key, which means funds have not moved. Sweeping simply means taking all the funds from one address and moving them to a new address. This is a transaction on the blockchain and will require a fee.
Sweeping is the easiest way to move funds from a paper wallet. Many wallets have an import or sweep feature. You can do your own research on that as this is not the forum for product suggestions.