I recently brought down the remains of a mostly-rotted tree from my
yard. It had snapped during the winter in a windstorm.

Cutting it down was pretty easy. I sawed very low to the ground just
using a bow saw, then a strong friend and I were able to push the trunk
over, snapping it at the cut.

What to do now with the stump? I don't want to pay a stump remover if I
can avoid it. Money (probably $75) isn't the big issue; the big issue
is that they'll then make a massive hole and dirt spot in my
otherwise-immaculate front yard, and that spot will be a bear to get to
look nice.

A few ideas I've had:

a) Flood the stump remains with water and just attack it with a hatchet
or a wedge and sledge hammer.

b) Perhaps put some gasoline or charcoal lighter on it, and burn it.

c) Just let it slowly rot over years.

The roots aren't an issue. The tree had been dying for years before it
snapped, and the roots are well underground. The remaining stump is
maybe ten inches in diameter, and extends to a maximum of two inches
above the surface of the lawn. I just want to remove it for safety
reasons (don't want kids to be playing around it and fall and bang their
heads, or to trip over it) and esthetics (I have a large green lawn,
with this whitish-yellow "spot" on it where the stump is).

Ideas?