The Paws Paws came from 81EMM and 82EMM and were already of known anti-Federal sentiment. (Splitting hairs, anti-Federal but not necessarily disloyal). They were an experiment tolerated to protect against both Jim Lane-type Jayhawkers, and Anderson-type bushwhackers. Protect hearth and home against all the bad guys. Then along came regular Confederate officer Col. John C. Calhoun 'Coon' Thornton, a perceived good guy, into their midst. They joined him because of opportunity, not likely because of some oath being bandied about most of them weren't required to take at all because they weren't EMM officers or non-coms.
Where the Paw Paws made their mistake was after they went over to Thornton, instead of heading south post-haste with their Union arms and equipments and laughing all the way to Arkansas, they hung out around Platte City and had a party, literally, during which they were surrounded and wiped out. Surviving defectors were dispersed and hunted down piecemeal, and shot down like dogs, with Coon Thornton engaging in behavior which all but destroyed his reputation during the era (but strangely isn't spoken of in modern historiography).
The phrase Paw Paws, originally specific to 81EMM and 82EMM, became genericized and applied to any considered EMM unit threat and likely (undoubtedly in my opinion) accelerated the broader EMM purge under SO 126. I imagine it ordinarily would have taken months to gather the lists of oath-takers from each of the far-flung county clerks, which then would have had to have been cross-referenced with thousands of names from EMM rolls to identify the 838 non-oath takers. But instead of months, it took just days. 18 days, to be specific, illustrating the urgency of the matter.