then write down the seed phrase, not individual private keys
It makes no difference in this case, private keys are software independent.
Maybe I have an address generated in electrum but I don't want to use electrum after that.
Have you read the answers above this?
As far as I understand, you don't have to use Electrum to recover addresses from backup seed phrase.
...you can use any open source piece of software with two very minor changes as explained by pooya87 above to restore an Electrum seed phrase. For example, with
https://github.com/iancoleman/bip39, simply open src/js/jsbip39.js, change line 116 to
return true; and at line 144 change the word "mnemonic" to the word "electrum". The derivation paths will be different (m/0 for legacy and m/0'/0 for segwit), but it will generate your Electrum addresses just fine.