Hiya!
Nope, you don't have to do anything to the sky box at all. Just get the new telly, position it, switch it on, and tune it into the various channels. Depending on how you connect 'from' the sky box 'to' the telly, means what you'll have to tune/connect on the back of the new TV. If you use the simple SCART connection, then make sure you know which SCART socket (if it has more than one) you plug into so you can choose that from the Telly remote to watch the satellite box on!
Basically, the Skybox is 'dumb' to what Telly you watch it on.
cheers, DtM! West London & Slough UK!