Got some more information last weekend from Ryan Thompson, who learned the tune and brought it to New Hampshire years ago. The tune was written for competition in a fiddle contest in Iowa in the early 80's, and was originally titled "The Eskimo Waltz." The name "Ookpik" was given to it because, although the meaning was unknown, it sounded like a good Innuit word. Ryan couldn't remember the name of the composer. Do I believe Ryan's account? Yep. I looked for "Eskimo Waltz" instead of Ookpik, and found:

A midi here, and dots here.

The tune was composed by Frank Rogers.