The people are the Inuit, an individual Inuit person is an Inuk. Those are the terms that should be used.
It's also correct that "Inuit" doesn't encompass all Indigenous peoples of the Arctic... but it doesn't have to? I don't see why you need such a term. If you want to talk about the Yupik people, use that term. If you want an all-encompassing term, use "Indigenous peoples".
Even if, for whatever reason, you need a term that includes these ethnic groups, but excludes other indigenous peoples, then why does it have to be "Eskimo"?
As a white person, I'm an outsider to the situation so I'm going to take my guidance from Inuit groups themselves, and they object to the term. There's nothing complex about saying that it's a bad idea to call a people by a term that they themselves consider offensive.