I don’t have a clear answer on your question, but can share a few ideas you might look into as well as reviewing the literature for any evidence of how others have defined this group.
Based on these enumerator instructions for 1860, I would expect hired hands who lived in the household to be listed after children or other relatives:
The names are to be written beginning with the father and mother, or, if either or both be dead, begin with some other ostensible head of the family, to be followed, as far as practicable, with the name of the oldest child residing at home, then the next oldest, and so on to the youngest, then the other inmates, lodgers, and boarders, laborers, domestics, and servants.
Because ordering is important in historical census data, CBPERNUM and/or PERNUM may be helpful as well as referencing the RELATE value of the preceding person in the household roster when looking into this. You might use OCC to get at identifying hired hands too. For example, there may be “other relatives” who report “Agricultural laborer” as their occupation and might be considered hired hands, though I don’t know of a way to determine if they are working where they reside or elsewhere.