I can do it with the water in the pool, though maybe a little lower than yours is in the pic. However, something's just occurred to me :idea: - the faceplate screws may be the only thing holding the skimmer to the wall

If this is the case, you'll want to take the water down below the skimmer before changing the faceplate. When you close the pool would be a great time to do both of these (**
make sure that the aquadoor faceplate will match up with your skimmer - both size and screw configuration! also get a new gasket for behind the faceplate) Having the water down will also make it easier to get the holes to match up - because the water will be just below the bottom holes, it's pressure should keep the liner from shifting much
I know you want the door to keep from having to lower the water every fall, but this is a 1 time deal and gets you the aquadoor and the liner patched all at once - loosing 6 - 8" of water for this sounds reasonable to me

Please do install the 'door' even though the water will be low when you cover the pool, the rain and snow that collect on the cover will force water into the skimmer - no need to loose more water
Looks like you have a "J- hook" liner - out and back in should be easy with the water level below the skimmer. Getting the holes to match up shouldn't present problems, the liner can just be pushed or pulled into position.
If you have any more questions about this, please ask (but not next Sat. - my annual golf tournament and if I do get home fairly early - I probably won't even be able to see the computer screen, let alone type {it's the S.A.D -Swingers And Drinkers- invitational} :lol: )