No problem.. Just hold the hatchet right under the head with your trigger finger on the side of the head and rest your fingers from the other hand at the base of the grind (to give some more downforce) then push the edge gently along an oilstone.. Give each side around 10 strokes then change edge and repeat. My £5 Draper hatchet got really razor sharp (ie as sharp as a good day on my S6!!) in about 20 minutes like that.

You could always use the mouse mat trick too- that works well on hatchets and gives them a nice shiny polished scary looking edge!