Is Zote a Vessel or void being? More signs point to "no" than "yes"
1) Unlike a vessel, his face doesn't seem to be a mask. There is a distinct mouth, a detail that all vessels seem to lack as they're always wearing mouth-less masks, as well as 'detailed non-circular eyes'. This makes him more comparable to Elderbug and even so, the journal entry for broken vessel implies that it (the broken vessel) was designed to look similar to the bugs of Hallownest, so it's reasonable to assume that bugs can naturally look like Zote and Elderbug. Probably the "Everyman" of bugs.
2) Additionally, as an obvious joke character, him looking similar may be part of a joke.
3) Whenever Zote takes damage, he doesn't release "black particles" that void beings tend to release. This can be seen whenever the player character takes damage, along with many other void beings.
4) When Zote is killed or defeated, he never leaves behind a shade or any direct indication of it. He doesn't melt like the collector or change shape in any way like the pure vessel's tendril attacks.
5) While the collector kinda talks, none of the vessels seem to talk, implying that if he is made of void, he is not a vessel, even though the kingsmoulds don't seem to talk either. But every void being has been made with a purpose and if not a vessel, then what is Zote's purpose as a void being? Void beings seem very "programmable" and typically lack personal desires. The other thing is that if he were a vessel, he would've tried to fulfil his 'programming' and take the hollow knight's place, even if he dies trying.
6) It's shown that he doesn't come from Hallownest. "I came to this kingdom to fulfill a promise..." this is found twice with the dream nail, so he isn't lying.
7) (Edit) New point. If Zote were a vessel, a lot of his dreamnail text (and other bits of dia/mono-logue) wouldn't make any sense. If he lived in the abyss, got out and raised himself, he wouln't mention a thing about other kingdoms or proving anything to his own parents because he wouldn't know such things. If he isn't a vessel and was in fact raised by the pale king, he wouldn't claim to come from another kingdom and if he is making the incorrect assumption that hallownest is a separate kingdom from its original state or the white palace, he wouldn't comment on hallownest reminding him of home because both of those would've been more prosperous in comparison.
In short: I see no real evidence for Zote himself to be a void being and a lot of evidence against it.
I vote Papyrus. Speed is equal but Zote is clumsy, unskilled and not very smart while Papyrus is at least a skilled combatant. If he tried to avoid the danmaku which he has zero experience dealing with, he would likely trip over, then get soul-struck multiple times over. If he teleports, he's falling and he can't seem to teleport in mid-air, therefore he's moving and can be struck by blue attacks, even if he understood them. Blue attacks will also catch him during his methods of creating shockwaves by falling, jumping or tripping. This danmaku should be able to rapidly clear spawns as well.
(PS: This is my first comment)