Coinigy is an interface, not a wallet. Coinigy has no access to your private keys (or public keys for that matter). The private keys are being stored by your wallet and /or exchange. Some exchanges have refused to support bcc because it is a maverick coin that is bad for the cryptocurrency image and ecosystem, I agree with that sentiment.
RE: How am I going to deal with Segwit and BitcoinCash BCC? Should you get comfortable with taking loses?