How can I measure of there is enough stub to rechamber to the shorter cartridge?

Use a vernier caliper to find the start of the chamber. That's where it will be cut off. Then measure the OD of the cartridge and what will remain of the barrel. You need about .250 inch of wall thickness surrounding the cartridge.

You will need a fat barrel shank to do this as you will have to cut off the entire old chamber area. As Speer said, just make sure you have .250 or so over the new chamber and ream away. That was a song from the 50s, BTW. The 6.5x47 uses the standard .308 case head size so as long as you have enough to thread, you might be fine. What barrel are you doing this on?

From memory I recall it to be a Krieger #5 profile which is a heavy sporter/light varmint type of barrel. It looks like it could be borderline.