Norse Dwarfs are not followers of chaos.
Generally I think a similar distinction would be between the Traitor legions and rengade space marines. Both have fallen out of the mainstream of the Adaptus Astartes, but not all renegades follow chaos.
Admittedly a lot would join chaos, but some renegade SM would remain space pirates.
So in theory it would be possible to have renegade CD that are a cult to nurgle. They would be ‘Chaos Dwarfs’, because they were born as such (their race doesn’t change). They wouldn’t be part of the CD society, and would most likely not live close to any cities in the Dark Lands (in a cave system in the mountains near high pass, or a small fortress in the Howling Wastes for example).
Mutant dwarfs would be a different matter, and more unrealistic. Most Dwarfs have an in built sense of self destruction if they are deeply shamed (becoming slayers). If they are thinking of becoming slayers simply because their beards were cut off, they would certainly do it if they became mutated.
A cult of mutated Dwarfs would have to be VERY secretive, because the Dwarfs would cut them down the moment they knew (as in Orcslayer), not even giving them a chance to redeem themselves as slayers.
I could see the CD becoming confused if they were blessed/ born with a bull like mutation, but were sickly and diseased. They wouldn’t know if it was Hashut or not.