Web API and Skills are offering an easy and fast way to use external Webservices.
Unfortunately this is not possible if you need a proxy authentication and therefore you'll get message like
Internal : Unexpected error Error during Web API HTTP Request
HTTP Status Code: 407
HTTP Response Content: <HTML><HEAD>
<TITLE>Access Denied</TITLE>
There is a workaround of using HTTP and REST VBOs instead of Web API, which will allow to set Proxy for a request, but this means that you can't use Web API and Skills here. This will a mean lot of more efforts in implementation of many use cases.
So in our opinion it would be a very good feature to have such an option also für Web API and within Skills.