Fake missing network connection for single app
You can use Xprivacy for that. In case you don't know, this is an XPosed module (available from the XPosed repo) dealing with privacy related permissions; details can be found in its XDA Thread). Instead of simply blocking access to the internet, Xprivacy fakes its inavailablity. To be on the safe side, you additionally can block internet access for that app using a firewall like AFWall+ – cannot hurt.

Side-effect: You can block/fake a lot more – e.g. your location, device IDs and other things. This can be done by defining a fixed value, or even in "random mode" – having Xprivacy either randomize data on boot, or even on each access.