Funny you mention this, just yesterday I was salivating over pics and video of the cold steel poll axe, and thought I could use the method you describe to make my own.
I have access to cnc milling machines so I would cut a shallow slot in the pipe first, so the blade and whatever else (could use this for mace flange thingies too) can sit flat and be welded more securely and accurately. I have a short piece of steel pipe that actually has an inside taper, it's about 2" inside diameter, a taper is nice otherwise you have to use screws or something to hold it onto the shaft.
Anyway, I think it's a good idea, but have limited experience with welding. How tough is the weld going to be?