@Dusksong@A Tattooed Girl How would it be obvious he's lying? Nobody here has ever met each other before, so they know nothing about one another. As far as I can tell (it's certainly the case with Shade and Razor) the only reason people think Jackson is part of the Regime is because he's currently wearing the uniform. Had he not been wearing the uniform in the first place, he'd have made a very different first impression. Unless a lie is particularly outrageous, whether or not it's obvious you're lying depends on good you are at looking and sounding sincere.
If, for example, Jackson claimed that he was never part of the Regime and just stole the uniform off a dead soldier to have something warm to wear, that would be quite believable to Shade. She's done similar things in the past, though she usually uses uniforms for kindling. Lying would come back to bite him in the future, but right now Jackson wouldn't be thinking about the future. He would be thinking about "how do I stop this Sneasel from tearing a big hole in my throat?"
It's Tattooed's decision of course, but trying to knock Razor off is a bad idea for two reasons: Razor has his claws right against Jackson's throat, and Shade currently has a gun. She's not trigger happy, but she wouldn't take kindly to somebody attacking Razor. Talking them down is the safest option.