My immediate hope was that you meant halfling slayer in the same way troll slayers slay trolls.
I'd say run his as a slayer rules wise, it is a state of mind as much as an actuallity. So go with the same rules.
Howver I would have any dwarfs he meets rolling their eyes and treating him as a loon for trying to be a slayer.
Good old fashioned predudice - 'you ain't a dwarf so how can you be a slayer?'
Any dwarven slayers he meets would probably be mortified and indignant and may even he angered and insulted by his belief that he is a slayer.
Although proving his worth by deeds may downgrade this to just sighs, mutters and snide comments (which is probably not much better than a halfling would get from a slayer in general)
And you can imagine the derision any Human warrior types would hold him in…