If it is needed soon, fix the new handle to the axe a go to work. But be prepared to have to readjust it after it dries a spell. I have one axe with a conical threaded wedge which allows easy extraction of the wedging system. If it is not needed directly, by all means dry it slowly, three years should do it good. I sealed the ends of two new handles and stuck them in the car for part of the day, didn't see any noticeable or negative checking happening, I have not set them to their heads, yet. Nice to have handles on hand.
I have another axe with the big wooden wedge still hanging out, just in case I need to remove it. It has been that way for a few years.
