Because I am a Cheapskate ...

... I don't want to pay transaction fees to move my cryptocurrency from the wallet I use now (Coinomi) to the wallet I just installed (Edge).

It seems to me that as long as I'm using non-custodial wallets, my seed phrase and/or private keys should be usable to simply make my coin balances appear in the new wallet. In fact, I think that's exactly how it worked when I moved from Jaxx to Coinomi a long time ago.

But I've forgotten exactly how that worked, and damned if I can find an easy tutorial on it now.

Anybody got simple, easy to understand info on that?