I don't know much about hammers so I have no suggestion about which hammer is best to use sorry. But I think I would hammer the computer and not my head... Using iWebSites
Open iWebSites and you get the list of your sites appearing under "All Sites"
Hit "New Site"
Select the site (it will be called "New Site" by default) and click Open
Now you will be working on the new site. If you want to work on the old site close iWeb, open iWebSites and from the list select the old site and hit "Open". Now you will be working on your old site. To switch back to the new one just close iWeb re-open iWebSites, select the new one and hit Open.
When you have the new one open you will not see the old one and viceversa if you have the old one open you will not see the new one. However they are still there. They didn't wipe-out. You just need to access them through iWebSites.
(I used iWebSites 2.4 and iWeb 1.0)