The Third Place reads
David Cerbone's "Heidegger and Dasein’s 'Bodily Nature'", on why embodiment cannot be a part of Dasein's essence.
Another line of argument is that Dasein cannot be reduced to something present-at-hand, and so embodiment cannot be part of the analytic. Again, he assumes that the body is nothing more than a present-at-hand thing which Dasein occupies. Working on these assumptions it is no wonder that he worries about dualism sneaking in. Similarly, organs (and thus the body) are defined in the way that they differ from equipment, as he once again assumes that the body is a mere physical object. If the body were part of the existential analytic it would surely not need to be carefully distinguished from equipment, which is of a different kind.
I consider the body to be part of Dasein, otherwise Dasein wouldn't be finite.