Interesting question. I think I'll go and add explicit support for proxies to NetherPanel to facilitate people in your position.
As for you, I doubt WAU has explicit support for proxy servers and authentication with them. The best thing I can think of for you to do, be it as a temporary workaround or permanent one, is set up a local proxy server that uses no authentication and simply forwards and requests to it to your real proxy server; then set up your PC settings such that the local proxy server is used instead.
This kind of thing is done often by people that have local ad filters like proximitron. Proximitron is a local proxy where you can configure your real proxy in. All web requests you make should be configured to go to your local (proximitron) proxy which then makes the same request to the real proxy and filters ads out of the reply.