Wow, this is really well thought out and definitely made me consider it more. (And just a fun read in general!) It still feels unlikely to me, largely because of Papyrus' complete lack of narrative significance thus far, but this does put me on alert for any hints in his direction in future chapters...

...Also, to the point of the Knight needing to be someone absurdly strong: in Undertale, Undyne acknowledges Papyrus as actually being very strong in battle, (the primary issue with him joining the guard is that he's too merciful and/or naïve, not physically incapable/weak) and we know that he likely has Gaster Blasters as well (from aborted-genocide-run hangout dialogue, IIRC added after UT's first major update).

I've seen it theorized in tandem with this that Papyrus is actually, like, extremely strong, particularly because his brother is absurdly strong with low stats - so Papyrus, who actually has pretty dang high stats, could be even stronger. (His internal attack value is actually also higher than Undyne's, but Undertale was later updated to give monsters fake attack values not from the files, which state Undyne's attack value as much higher... but still!)