An easy way may be to just run the mysqldump command line program.
Unless your ISP are really bitchy -you should not have a problem using this. You can specify all the username, password, port, server etc on the command line.
You can then capture the output, and dump this to the browser as a file to be downloaded (using approriate content-type headers etc).
As long as you make sure this page is nice and secure (htaccess, or your own username login script), then I think the solution works best all round.