The answer to this actually depends on one factor that we'll need to go through.
Is there any Pokémon in your team which can take advantage of Toxic Spikes?
Nidoking and Drapion are the only offensive Pokémon in your team. Now, Nidoking's main checks/counters are Blissey, Piloswine, Rotom-Wash and Slowking. Say that you run Toxic Spikes. So out of the aforementioned Nidoking checks, only Slowking and Piloswine would get affected enough by the said move. This might be confusing, so let me explain. What I mean is, that only Piloswine and Slowking would get affected the most by Toxic Spikes, sometimes this much that they become shaky checks to Nidoking. Rotom-Wash is immune to Toxic Spikes (and can Defog it off, too), and Blissey is a fatass Pokémon that also with Natural Cure so no comments. Now Slowking also has Regenerator, which helps a lot verses Toxic (or normal Poison), and if you catch it with only one layer of the Toxic Spikes, it (Toxic Spikes) won't be that good of a move choice. Ergo, you might just want to run Toxic on the Toxapex if we look at what the Nidoking likes, as, overall, it would help more.
Now, the Drapion. As far as my Monotype experience goes, that's a little weird set. I've usually seen the RestTalk set (chad set henceforth) which phazes a lot and is a nuisance. Other nice set is Scarf, which can set Toxic Spikes on their own and is a nice revenge killer. Swords Dance is a nice thing, albeit rare, and well, I’d actually advise you to run any of the aforementioned sets. Granted, Choice Scarf Drapion is more of a Dark-type Mono thing, I’ve tried it on Poison- and yeah, it worked. Now if you choose any of these, I’ll tell ya one thing. The chad Drapion set is actually very good on these type of builds, but that’d make your team very similar to the sample, tbh your choice. If you do that, though, you won’t have the moveslot left to fit Toxic Spikes, so you can do Scarf which usually has a free slot, so you’ll have Toxic Spikes and Toxic on one team.
So you can do Toxic Toxapex, and Toxic Spikes + Choice Scarf Drapion (which also runs Toxic), or Toxic Toxapex with the RestTalk Drapion.
Hope it helps!