Can I have it outputting to two different TVs (on separate occasions)

I'm currently setting up a video game station, with a CRT for older consoles and a modern TV for the newer ones.

I own a 25XX PS3 Slim.

As I don't own a PSX, the PS3 will serve to play widescreen 720p PS3 games, and old-school 4:3 PSX games.

So as not to have to mess around with cables all of the time (I just want a media setup that works without meandering), I'm thinking of plugging the AV Multiout cable into the CRT, and the HDMI cable into my modern TV. Only one TV would be on at a time, depending on what I'm playing.

Is this possible? Is there a different way to make this possible? Thanks!