I'm guessing if an intelligent monster without hands (e.g. a Sandpoint Devil or similar) could try a healing check to stop bleeding
Not likely. But stabilize rules exist.
Stabilize happens only when the creature is already dying (and in my opinion does not stop bleeding either). I'm asking if a creature could stop bleeding in some way if it does not have access to any form of magical healing
Does it have some kind of appendage? If it can put pressure on the wound I'd say it can try a heal check. It won't be easy, but they can try.