I don't know how much help I'll be as I can't really give you full recommendations or specifics, but let's see how this goes.
Firstly, to be fair I don't use WYSIWYG editors or anything of the sort (text-based only). So I'm not extremely familiar with what all is available. I don't think I've ever seen a server-side implementation of a website editor builder that can be integrated into an existing site. There are editors and builders out there, but generally they require that you build your site using them, not plug an existing site into it.
However, there are client-side solutions (actual programs) such as Dreamweaver (or a number of alternatives that I'll list in a moment), which can allow you to connect via FTP to a site and edit the pages in a simple WYSIWYG editor, and then of course save and re-upload the files. So based on what I know in this area, I feel like this would be the best solution for you.
Dreamweaver is obviously going to cost you (and Adobe is a bit pricey in my opinion, even with the new CC licensing), but there are a number of other options that you might like better:
Microsoft Expression Web 4 (Free)
Aptana Studio 3 (Free)
KompoZer (Free, a bit outdated)
There are still a number of other options, but those are 3 that I know can do what you want and are easy enough to use.