It's not enough to just not connect to the internet. There should no longer be a possibility to do it. You need to make sure that you don't have the required hardware to ever establish such a connection. That entails the Ethernet and WIFI card.
I never thought about that before when I tried it the first time. I just input in the wallpaper and a bunch of words that say "Do not connect to the internet" if there's someone accessing my air-gapped laptop. That's a better way of doing it, making sure no connection. Well, I just opt for a hardware wallet when I had the chance before, never regretted it.
If you do that and import keys that were once used with a hot wallet, they will remain as keys that were associated with a hot wallet. You are just using them in a safer environment now, but they are not secure, and remain potentially vulnerable depending on the software they were generated in.
It's better to be safe than sorry. Paying for the transaction fee is better than paying with your whole wallet.