I think it’ll be “hasn’t we?”. But I feel that it’ll be “don’t we?”.
Also what is the question tag of, “Man is mortal _____?”
Will it be “isn’t he?” or “aren’t they?”
The contraction is messing you up.
Everyone of us has to cooperate, have we not?
Man is mortal, is he not?
Men are mortal, are they not?
If you use the contraction it obscures the form that works.