Though there is a chance the date isn't on there - it is on most of the registered axes, but not all. As far as how to correlate the reg number to the year made, I am sure there is a way to do that, however I am not sure where to point you to or who has that info. I do not, sorry.
One thing that might help, or might not, is the fact if it has labeling/etching on the back. If it says Kelly Axe Mfg Co, then you know it is pre 1930. If it says Kelly Axe and Tool Works, then it is post 1930, and if it has True Temper on it, then it is post 1949. Hope this helps. Might not. Good luck.