Does the customer have an internal DNS server?
Perhaps they can setup qlik.company.com to go to the internal IP on internal DNS for employees in the company, and to the external IP on their public DNS server for outside people like you.
Everyone would then just go to http://qlik.company.com/qlikview
Nice to meet you here..
I don't know if you managed to find the solution. In case not, you can try this:
Open QlikView Enterprise Management Console > System > Setup > QlikView Servers > QVS@172.x.x.x > General > External Linking, fill in the 10.x.x.x ip address. Click "Apply".
Hope it works!