Maybe they were "skirmishes" by European standards, but not by standards of the colonies at that time. At the start of the War of Spanish Succession there were only ca. 300,000 white and black people living in European colonies in North America* (the majority in English colonies). Native American tribes were also not exactly very numerous, for example the Iroquois Confederation numbered 70,000 people in 1690:
https://en.wikipedia.org/wiki/Popul..._peoples_of_the_Americas#Estimations_by_tribe
So even a "skirmish" involving a few thousand men on each side was large by North American standards of the 1700s.
*Only counting those in colonies to the north of Rio Grande (excluding Mexico, Central America and the Caribbean).
This low population of North America in the 1700s is actually one of the main reasons why the conflicts happening there were minor and why that also does not qualify the Wars of Spanish/Austrian Successions as World Wars. Furthermore these skirmishes did not have any real impact on the course of events of these two wars in Europe. They just happened during the same period, but had little to do with the matter of Spanish or Austrian succession, which was the cause of the war. I suppose that the Iroquois had little idea of where Spain was, and may never have heard of the House of Habsburg.