I'd take it slowly Jon. If the cat gets more confident with you, putting it into a cat basket and toting it off to the vet to be scanned would be traumatic and make it very wary once more. It might even scarper completely.
It might be an idea to put a post in your local magazine or on a noticeboard in the local shop, with a description.

Have the pair of them been coping in the bitter weather? It breaks one's heart to think of homeless cats with no warm fire or shelter in this cruel weather.