I would think you can do a 'stand-alone' replacement with 2.7.
You would need to keep only the wp-config.php, as in the Upgrade Instructions but I would leave wp-content Folder alone - the stuff in there should be fine aside from any Plug-ins that may need updating, which you would likely be advised of anyway.
Is there a lot of trash in your ROOT directory? I have ONLY the ones from the WP 2.7 upgrade, plus some [-orig] versions I named so as to save incase I wanted to swap back to that file version. But all the files in there that are being used are straight 2.7 version aside from my Config which I updated with the Secret Word thingy at about ver 2.6.3.
My first version was before 2.3 (my first upgrade was 2.3) and I recall I had to ditch all sorts of files and folders - which in my Direct-Admin setup means file by file and folder by folder!!
I still have not managed a satisfactory WP Auto-Upgrade but mebbe 2.8!!
The more I have experimented with WP the more I realise, once it's working, it's almost as foolproof as people without problems say! The Root Directory, wp-admin and wp-includes are all you need for WP 2.7 to work, as such. After that the 'pretty bits' are really in your database, all your 'stuff' and graphics, I think.
They say scary stuff in here (the Forum) about security and the need to keep on top of Upgrades. Also the need to rely after WP 2.7 on the WAU Plugin. Haffunt gottit ta wurk yet ggrrr
TIP: Don't miss any files in the upload to your server. I missed ONE template file !! Maxwell Smart said it all!