try to look for a "hunter's hatchet/axe" or a "forest hatchet/axe". Its easier if you can just look at catalogs of manufacturers like Gransfors and get an idea of what you want as often you can find the name hatchet and axe used interchangeably in some sale catalogs, manufacturers are more precise. Generally though an hatchet is a small axe, so shorter in lenght and lighter head. To confuse matters a bit more there is the hand axe which is small like an hatchet but the head is shaped differently but people still call it an hatchet. There also are "boys axes" which are lighter axes, lets say something sometimes less than 2lbs head on a 28inch handle. You can make one yourself buying the head you need and fitting an handle of the desired length that you bought separately or making the handle from scratch.
If you would want to dig a little deeper you could look for a tomahawk. Let all the movie ideas about a tomahawk aside. Tomahawk is nothing else than an Algonquin word that means "hatchet" and if you get a colonial era french axe and the tomahawks traded at the time they are the same animal. Overtime they took two different paths differentiated in shape of the eye etc and now we have a very different image in our head of what a tomahawk is while in origin was just an axe with a light head or an hatchet with a longer handle, same result. A search for tomahawks online will pull up a lot of garbage too but some companies still make "colonial style" heads for tomahawks that are still great for bushcrafting.
Don't just use the longer handle idea just to go around a lack of skills as that might catch up with you, if you think you're gonna put the other hand in the way then you need to review your technique.
