It's not perfect but how about the following:
Create a cover page that has a "Website down for maintenance" message.
Create a temporary url redirect (302) to redirect the all pages to the maintenance page. This will tell Google it's a temporary change and not a permanent one (https://support.squarespace.com/hc/en-us/articles/205815308-Creating-URL-redirects)
Make the edits to your pages. Test.
Remove the temporary url direct. Go-live.