Oh, sure, there's no reason a psychopomp has to be necessarily associated with a specific religion. They could always appear as someone close to the dying person - a loved family member, a friend, a personal hero. They could even have their psychopomp appear as themselves, bringing to mind the old myth of the Doppelganger, and it'd be an excellent opportunity for some soul-searching.
Alternately, the psychopomp could well appear in a religious context (the angel of death, or Hermes, or Thoth and Anubis, or a valkyrie, or whatever you like) and imply that they have that appearance because that's what the dying person expects or wants or needs to see, rather than what the psychopomp "really" looks like.
If you are going to imply that all religions are true, mind you, how much work you'll need to do depends on how important cosmology is to the story. If it's just a passing reference, then it's not necessarily a problem, but otherwise you might have to make some changes to the established canon (and risk alienating members of any living religions you mess with, or mythology buffs).