It's not that hard for it to be Danish, or Dutch--
It can be plausible, even with later PoDs than have been discussed.
The area was first mapped by Frenchmen, Grossiliers and Radisson. The powers that be in Montreal were quite comfortable with established trade routes via the St. Lawrence and saw the route through the Bay as undesirable competition, so Grossiliers and Radisson went to Boston and started working with the British (one or the other of them ended up opposing the British later).
What if they pitch their business proposition to Dutch, Swedish or Danish investors instead, meeting them in either New Amsterdam, the Caribbean or Europe?
Sweden and Denmark would certainly see themselves as markets for fur products, and so might be interested in the bay.
Keeping it can be a challenge, but its not implausible at all. Yes, any determined French or British effort to take over the area and hold it would be irresistible to the Danes, Dutch or Swedes, but lucky alliance politics or higher priorities for London or Paris could see the Bay held (or ultimately restored to) one of these alternate northern European colonizers over the long haul.
Ruperts land, the shores of its bay could end up as more the focus of Scandinavian migration to North America instead of Minnesota and Wisconsin.
