Your program doesn't use HTTP. Your MySQL server doesn't use HTTP. So if you want to use an HTTP proxy server to connect the two, you also need two other proxies.
On the inside you need something to convert the JDBC protocol to HTTP. And on the outside you need something to convert that HTTP back to the JDBC protocol.
I don't believe those things exist, at least my 30 seconds of googling didn't find anything. Read this post and all the responses to it:
http://lists.mysql.com/win32/18177
And if I were you I would start looking for some other solution.