Already being done, check this site out
http://www.mosquitorestoration.com/
I had the opportunity quite recently to visit the hangar at Ardmore airfield, just outside Auckland, where this job is being done. The work is to an extraordinarily high standard and the first of several aircraft should be ready to fly in September. All woodwork is entirely new, but virtually all the mechanical parts are genuine and original. They have built jigs for manufacturing both wings and fuselages and have used both modern and traditional adhesives.
They also have a complete fuselage of what I understand to be one of the '633 squadron' Mosquitos (a 2 seat side by side version), but this original assembly could never be flown again. Instead, they intend to rebuild the aircraft with new components built on the jigs, so they have a little production line going.
I promised not to publish any of the photos that I took but there are quite a few on the Avspecs (the company who are doing the job)
website. What I saw was virtually a complete aircraft, with undercarriage cycling in progress on the day that I was there.