Electrum is an open source and non custodial wallet that gives your own private keys of your bitcoins. You are able to fully access and control your bitcoins as well as Bitcoin transaction broadcast including customized fee rates.
Safe or not, it starts with how you download, verify and install your Electrum wallet before using it for generating your new wallet.
You can do it by either: Sweeping like you described, or simply creating a new wallet by Electrum wallet software and manually sending your bitcoin from your old wallet to a new generated wallet. Both ways are safe but make sure your computer is clean and does not have virus. Using TailOs is good but I would like to make a note on importance of your device security status if in future you won't use TailOs.
[GUIDE] How to Safely Download and Verify Electrum.The paranoid user's security guide for using Electrum safely.After the funds have arrived in Electrum, I will transfer them to the Relai app, which is
linked to my IBAN bank account. This makes trading very easy.
I don't know about Relai app but I am curious that whether it is open source and non custodial wallet?
By an information of bank link, it seems Relai is not safe to store your bitcoin, honestly it's my guess as I don't know about Relai app.