In the meantime, I have overcome all difficulties and have successfully moved my WackoWiki to a new server. Let me enlist a few important things I have found out. Hope they might help someone someday:
1. Dump the sql - Database via MySQL on the old server.
2. ftp download all files from the old Wacko folder on your local computer.
3. make a new installation of your version of WackoWiki on the new server to be sure the new webspace and server are ready.
4. open wakka.config.php from your download (point 2.) in an editor and adjust the url of the new path of the new server.
5. ftp upload all files and subfolders on the new server.
6. If you have only very few pages in your Wacko, you might be able to just import the dumped database (point 1) via MySQL on the new server. However, it is probably too large as there is a file size limitaiton in MySQL.
7. Use the tool "Bigdump" (http://www.ozerov.de/bigdump/) to import the dumped database (point 1) onto the new server.
That's it! I did everything on a Mac and used the program Cyberduck for ftp. I didn't have to chmod anything.