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The WAN port needs to be connected to a modem, not another router, and the authentication would fail.
Are you a BT broadband customer at the moment?
You could use the Sky box as a modem/router and then connect the SH LAN port to Sky LAN port and use it as just a wireless access point.
A WAN port performs a totally different function to a LAN port. If you use the Sky box to do all the modem,routing, natting and PPP functionality you can just turn off DHCP on the HH, give it an address outside of the DHCP range of the Sky box and it will just behave as a 3 port Ethernet switch and wireless access point.
Edit: You may have to change the subnet that the Sky box uses as I believe the HH is restricted to using the 192.168.1.xxx subnet.