You can just swap TVs but you will still have SD from the TV2 tuner as you do now. FWIW, viewing SD on a HD TV varies between acceptable pq to just plain awful. You'll find that the pq of SD on your old SD CRT TV was much better than it will be on the new HD TV. JMHO. If you can get an HDMI cable to the new TV you can mirror the TV1 signal & enjoy HD on it. Same channel/same time as the primary TV of course. Use the component out for HD on the primary or pick up a powered HDMI splitter.
Ed