Updated answer for iOS 11 and macOS 10.13
Since iOS 11 it is possible to declare an object that conforms to the WKURLSchemeHandler protocol and register it in the WKWebView configuration: -[WKWebViewConfiguration setURLSchemeHandler:forURLScheme:].
Old answer
WKWebView makes requests and renders content out-of-process, meaning your app does not hear the requests they make. If you are missing a functionality, now is the time to open a bug report and/or an enhancement request with Apple.
As of iOS 10.3 SDK, WKWebView is still unable to make use of custom NSURLProtocols using public APIs.
Enterprising developers have found an interesting method:
+[WKBrowsingContextController registerSchemeForCustomProtocol:]
It supposedly adds the provided scheme to a list of custom protocol handled schemes and should then work with NSURLProtocol.