The 1903 Colt needs to be made again by someone.
That's easy to say, but not so easy too do.
In Browning's day, the highest quality guns (and Cot was a top quality maker) had parts that were machined from steel forgings. The resulting guns were great, but this sort of construction isn't always compatible with the kind of technogies that are necessary today because of manufacturing economics.
So first of all, manufacturers now are generally not set up to make guns the way they used to, and if they did so the resulting gun might cost as much or more then an excellent or like-new original.
And many potential buyers might insist that the hammer be at rest and not cocked while the pistol was being carried, and if necessary fired with a long double-action style trigger.
Personally I would be delighted if someone made a high quality clone of the 1903/08 Pocket Model, but any market study that Colt (or whoever) had made would tell them that the idea wouldn't work.