After some extensive testing and logging different cases with Qlik, it looks like there is a known issue with Websockets not being supported on latest iOS versions (after version 9.3.5) - Android devices are not affected. No matter which browser you install on the Apple device it will use in the end the same Safari rendering engine (this is the rule stated by Apple on the app store).
One good news is that it looks like Opera mini browser is supporting Websockets and therefore will allow a VPN connection when the browser is used to access Qlik Sense. We don't have a productive solution yet but testing is very promising.
All browsers on iOS are built upon a WebKit component from Apple. There are two:
UIWebView which is rather old and now only used by relatively obscure browsers such as Dolphin and Opera, but it does work
The problem in WKWebView has impacted ALL Enterprise Mobility Management (EMM) solutions, but has been resolved in iOS v11 (released September 19, 2017).
If the Mobile Device runs iOS v11.x, and the EMM infrastructure has been appropriately configured to support iOS v11, and the EMM Gateway (Airwatch's VMware Tunnel server) is running on Linux and configured to Tunnel (not Proxy) connections into your corporate network, then modern browsers such as Safari, Chrome, VMware Browser should all work. Android devices have not been impacted by the iOS problems, and should work ok.