Detectably British
I'm proud to be detectably British, and I'm proud that you are too. A UK brand can be a global brand, and many already are. Yours is one. And the URL fits the content, which is itself detectably British.
I don't think us.theregister.co.uk looks silly. It's clear what it means - "this is a section of a British site with some bits of special interest to Americans". Whereas "uk.theregister.com" can be misinterpreted.
Stick with .co.uk.