Stick with non-negative. The meaning
is clear, and more importantly, correct.
By analogy, consider the name given to
a list of things sorted in ascending order. Calling the list ascending
is only correct if you explicitly exclude the possibility of having
repeated values. If the list contains two or more items of the same value it cannot
be called ascending because
two things that are equal cannot be placed in ascending order with respect to
each other. In fact, such a list is properly called non-descending.
The negative/zero/positive problem falls into the same sort of trap. There are 3 categories of
number: Negative, zero and positive. Describing a set that
includes any two of the categories can be done by naming the two or by negating
the possibility of the third. Any other type of description would be ambiguous.