Here is a source for a verity of axes.
http://www.benmeadows.com/search/axeThe Rigger’s axe fits my idea of a great axe because it is short, sharp, and tough. It does not present the user the same problems an axe with a wooden handle presents. The head stays on the handle, after a few years the best of wooden handles suffer some shrinkage.
ESTWING® Rigger’s Axe
I own two or three hatchets. But the best one is a True Temper with a metal handle with a rubber grip. It has chopped wood and split game for over 40 years.
A word of caution, a short handled axe, also known as a cruiser’s axe, or Boy’s Axe has some risk in its use. A miss with a long handle axe many times plants the blade into the ground. A miss with a short handle axe plants the blade in the foot or the shin, or in my brother-in-laws case in the knee.
For a tight budget this might fit: Ames Boy's Single Bit Axe, 2-1/4 Lb
A safe axe must have a sheath. Or the cutting edge taped with Duct tape.
I own a couple of single bladed full size axes. One I re-handled and Epoxy the handle to the head. It is a good tool. The second one came out of my Dad's garage after he passed away. My younger brothers broke the orginal handle, and then did a poor rehandle job. I am embarrassed to have it in my shop. I need to buy and install and new handle the right way.