Celebrating Wildflowers website that there is in fact a specialist bee for squash: "native solitary bees of two genera, Peponapis and Xenoglossa, the so-called 'squash bees." From the photos shown there, it looks rather likely that the bee inside my squash flower is indeed a squash bee.
Squash bees have been shown to be excellent pollinators of zucchini and butternut squashes, among others. If numerous, they thoroughly pollinate all available flowers, rendering later visits of honeybees superfluous. Before Europeans brought honeybees to the New World, squash bees were busy aiding the adoption, domestication, spread, and production of squashes and gourds by indigenous peoples throughout the Americas. [quote is from the USFS site linked above]