The only way Nic's coin will ever need a new holder is if Nic dies. He and the Fallen in his coin are two peas in a pod, a match made in hell, anti-soul mates...they're absolutely perfect for each other, and 100% on the same page. I'd even go so far as to say separation could potentially damage even the Fallen because they're so mixed together now. In Nic's case, the Fallen didn't take over, they totally teamed up, all the way...they may as well be one mind now. That said, Nic CAN die under the right circumstances, so if it works for your game go for it.
Of all the other Denarians, only Lasciel or perhaps Namshiel really have the brains and the temperament to pull off such a plan. The others are either too stupid or too impulse-driven to manage it even with Nic's constant and direct management. So if it were to happen at all, it would be one of those two. As long as they pick the right host (like say a well-meaning but desperate activist sojourning in a third-world country in an attempt to better things) they won't need a cover story, and it'll make them even harder to find out...fewer clues to follow. Especially in Lasciel's case, she'd have no trouble twisting the good intentions of such a desperate overachiever with her temptations. Give it a year and odds are in favor that they'd be in full collusion with her even after they discover what the Denarians really are. Tessa's band might try a stunt like that with an unqualified Denarian in a poorly chosen host, but that's not Tessa's style anyway. She'd only do it for an opportunity to strap a bomb with weaponized anthrax to detonate during the first official debate...and that's stretching it. Nic would never let any of his band BUT Lasciel handle such an operation. In such a case, even discovering there's a problem is going to require a Herculean effort of investigation.
As for other groups such as outsiders...that's where the "checkered past" sort of thing comes in. Outsiders and demons can really only get at those who are already on the wrong side of good and evil. Most of those who're on the right side are still out of reach even at their most desperate and despairing simply because there's nothing to connect them to evil, not even common and idle knowledge. So, anyone who gets a helping hand from outsiders or demons is going to have a murky background that needs to stay hidden. Conceivably though, someone who went that route might very well be more dangerous than a host to Lasciel. She's not the most powerful of Denarians, and some outsiders and demons make any single Denarian look like a toddler. So the increased risk of discovery comes with a commensurate degree of potential.
Another interesting idea is perhaps a Lasciel-host Democrat running against an Outsider-backed Republican...or even vice-versa. The results could be VERY amusing indeed. And most importantly, which one do you try to stop first? Do you even have the time or capability to stop both? What happens if you do stop both and some piddly mortal replacements make an even bigger mess of the political landscape? Oh yeah...I'm diggin' that idea hard...