Small axes are available like the Brit infantry axe, and various belt/bag axes, they would probably have abot a 2" cutting surface and a poll there are several around with various names.
Seems like ya need a bit more than 2" to cut firewood. Are these type axes more for throwing ?
Depends on the size of the wood. If I was using to cut wood for the stove, yes. But for general stuff around a pack-in camp, it works better than you think.
One small hatchet i own that has impressed me is the Mohawk Axe as carried by RE Davis, TotW, etc. Inexpensive, based on 2 original pieces from NY and a real workhorse even though it's relatively tiny.
Mario