The word you're looking for is slouching, which describes a body posture whether the person is walking or sitting.
stoop is an action verb that means something like 'bend your body', so it doesn't work to describe posture unless used as an adjective, as in stooped (over). The same goes for hunched (not hunching).
The verb slouch is strange in that although it refers to a posture, the way we use it in continuous tenses makes it seem like it's an action verb: it isn't, really.
You're slouching.
Stop slouching.
In both utterances above, the speaker is talking about a body posture, not an action.
He slouched over to the fridge and pulled out a cold turkey sandwich.
However, in the sentence above, in the past simple tense, it denotes an action verb, where it means something like 'walk while slouching'.