iOS switch network configuration
You should look into configuration profiles.

Their contents are described here:

https://developer.apple.com/library/ios/featuredarticles/iPhoneConfigurationProfileRef/Introduction/Introduction.html

You can build two profiles, one with and the other without proxy, and you would be able to create a link to each. Add those two links to a single webpage, and then add that page to Home Screen.

That's two taps rather than one, though.

Another option is two make two separate pages, each with a javascript redirect to download the profile. You could then save each of the pages to the home screen.