Cable TV / RG6 Switch

I'm trying to figure out how to build a box that will allow us to connect to an IP device (Arduino / Etherdshield) and then control up to 16 F-Type connections as to whether they're connected through or not.

We're a hotel for timesharers - the EASIEST way to turn off cable tv service would be this way, if I could ...

I'm imagining:

F-connector -> switch/relay -> F-Connector

Can this be done, ya think ?