I started to post this as a comment (not an answer), but it became too long. I don't have a specific recommendation, but I'm very interested in the answer.
Based on my experience, true in-line editing (which is what you're describing) is notoriously difficult to implement correctly. What you see in most CMS's (and Wiki's) is pop-up editing (except they frequently call it in-line editing).
In this scenario there is an in-line Edit link that sends the editor somewhere else (to a sandboxed editing environment). After the edit is saved, they are returned to their original context. This is even used by the StackExchange crew.
Whereas true in-line editing does not remove you from your original context. Instead, as you describe the text simply becomes editable (in place) with a click. The only CMS I've seen accomplish this elegantly is Squiz CMS. I've never used it in person, so I'm not sure how fragile or buggy this is.
I have, however, used in-line editing plug-ins for WordPress and they were awful. The in-line editor would inject HTML into my page, ruin the design and the editor was extremely buggy & mis-behaved. I abandoned them after only a few minutes.
As mentioned, I would love to see an answer to this question and be proven wrong, but I doubt that you'll find a Wiki that implements in-line editing in the way you describe.