What is the meaning of the word 'skirmishingly'?

Answer 1

skir·mish (skûr'mĭsh)
*A minor battle in war, as one between small forces or between large forces avoiding direct conflict.
*A minor or preliminary conflict or dispute: a skirmish over the rules before the debate began.
intr.v., -mished, -mish·ing, -mish·es.
To engage in a minor battle or dispute.

Answer 2

A skirmish is a minor battle in war, as one between small forces or between large forces avoiding direct conflict or a minor or preliminary conflict or dispute: a skirmish over the rules before the debate began.
Thus the adverb means that it is acting as if it was a minor fight.