OK, I think I understand, but just to be 100% clear you're saying if I move my BTC from BitcoinCore to a new wallet, im then free to export the private keys on the old wallet without any risk?
This is true, in that case your coins will be stored in new wallet on new address which is controlled by new private key, which means that old address is empty and using that old private keys does not pose a security risk for your BTC.
Of course you should pay attention on that new wallet for BTC, always at least double check that it is legal source for download. In case of Electrum BTC wallet use only
https://electrum.org/#home and read about posted warning.
So I transferred over the coins to another wallet, and then I used the dumpprivkey command in debug of BitcoinCore to get my private key. The only problem now is almost every Private key that I try to sweep into Coinimi wallet comes back with the message " the private key does not contain any funds". I've had more or less the same amount of BTC in my wallet since Mt.Gox exchange flopped, but all Coinimi could sweep out was a .1 BCH. How is that?