I'm just curious: but why exactly do I have to transfer my BTC to another wallet?
I understand that this is a standard phrase for safety reasons in the FOSS world.
But shouldn't BTC and BCC co-exist nicely? So will this procedure do my BTC any harm or the sky will fall on my head or something?
I just want to be sure that the BTC wallet will be okay like in a "nothing did touch me" way and the other wallet will just use this extracted private key to get the BCC...
It's not just about whether you trust your BTC funds to the developers of the BCC wallet in which you will import your BTC private keys, but also about the risk of someone finding a vulnerability in the BCC wallet. They could potentially have access to your BTC funds as well. So you have to decide for yourself whether saving the BTC transaction fee is worth the potential risks.