I thought most Panasonic DVDRs passed through and external source (your Sky+ box) even in standby.
When you say switch off do you actually mean turn off at the mains or unplug it?
Left in standby I'm sure it passes through, mine definitely does - i know there are other forum members who are more familiar with recent Pannys who can answer this.
If the TV and DVDR have HDMI sockets come back other wise...........
In the meantime you can leave your DVDR turned on and left on AV2 as input.
In the set up you need to set Sky+ picture settings to RGB and 'scart control' to on
In the DVDR you need to have the AV2 and AV1 scart sockets set to RGB
You need to check that TV AV1 is the RGB enabled scart socket on the TV - it almost certainly is. If you turn on and play a DVD you should see an 'RGB' logo appear briefly in the top left of your TV picture.
These settings will ensure that you have the best picture possible.