Either you're 156 years old, or there's a typo in here somewhere!
Seriously, now, here are a few comments and you can draw your own conclusions....
The Army's standard hand axe, the M-1910, changed very little between 1910 and 1945. It was basically a Dayton or Forest pattern. What you have there looks something like a Shepherd's or Hudson's Bay pattern. Not saying it's not military, but it's definitely not the hand axe that was issued to almost every brand I can think of, from Infantry to Medical Corps.
There are some nuances to what I am about to say in different branches of militaria (e.g., Ordnance vs Quartermaster vs Corps of Engineers), but
generally speaking, serif fonts are associated with WWI, and sans-serif fonts are associated with Interwar and WWII, and that is definitely true of hand axes. WWI hand axes will have a large "U.S." stamp, but it always has serifs. WWII hand axes will also have a large "U.S." stamp, but it will be sans-serif. Your hand axe is sans-serif. However, again, generally speaking, WWII hand axes usually have an OEM marking and a date. Yours has a secondary marking, and that marking oddly has serifs.
In summary, in pattern and markings, it really doesn't follow the general guide.
I don't know anything about Civil War hand axes. The pattern sure looks older. But would it have a large sans-serif "U.S."? Maybe your friend was right.