You should be able to give them edit rights only to the module, currently that will still mean they have to switch to "edit" mode with the radio buttons, but won't give them any other rights on the page if you have the page configured properly.

We'll be looking at overhauling permissions for the Wiki in a future release, as many people have requested that we not have to grant edit permissions to the module in order to edit the wiki. You also might just choose the option to not use the DNN permissions and set the permissions manually to see if that will work for you.