In the dpp era, special Toxicroak was a very good set. Despite its physical set seeming and perhaps also being superior to its special set, special Toxicroak has the ability to break through and or to set up on more Pokemon while "only" losing potential hits on certain Pokemon, such as [email protected], Gengar etc. while hitting Pokemon such as Skarmory, Slowbro, Rotom-W etc. for much more damage.
In gen IV, the special set was much easier to counter than the physical set, but due to how the metagame has evolved, you could say that they are pretty much on par as the special set makes Toxicroak very similar to an Adaptability Dragalge with the ability to boost, however at the cost of some bulk.
Surprise factors aren't necessarily always a good reason to use a certain set over another, but once they create their own noticeable niche, they are most certainly worth trying out.
Special Toxicroak is definitely an interesting choice, but I must say, despite your mixed lure Toxicroak being very interesting, it won't work. Toxicroak has good offensive stats but they aren't high enough to split into both attack and special attack while retaining enough speed to function in this current metagame.
A more optimal take on a special Toxicroak would be:
Toxicroak @ Life Orb
Ability: Dry Skin
EVs: 4 Def/ 252 SpA / 252 Spe
Timid / Modest Nature
- Nasty Plot
- Vacuum Wave
- Sludge Wave
- Dark Pulse / Focus Blast
I think the moves are very straightforward. Nasty Plot enables you to boost Toxicroak's special attack to rather threatening levels.
Vacuum Wave is a STAB priority move which enables you to KO Bisharp, KO Mega Lopunny at +2 some other interesting stuff.
I believe we're all familiar with Sludge Wave's amazing power. Despite it not being as powerful as Gunk Shot, it obliterates physical walls that fail to resist it. Physically defensive Rotom-W is 2HKO'd by it and OHKO'd when you have a Nasty Plot up. At +2, it enables Toxicroak to defeat every fairy type in the game, which might not seem that impressive due to the fact that Gunk Shot does the same unboosted, but the fact that it can set up on Pokemon like Rotom-W make it easier to pull off, and it's more reliable. It also KOs Mega Slowbro at +2.
Lastly Dark Pulse rounds of special Toxicroak's coverage and enables it to hit psychic types for great damage. An interesting fact is that if you happen to be at +2 and something like Metagross is yet to mega evolve, you will outpace and KO it with D-pulse, but I do admit that this is a pretty rare scenario. Focus Blast is also an option to hit the likes of Scizor, Ferrothorn, Skarmory etc. for incredible damage as it KOs Skarmory and Ferrothorn after Stealth Rock damage while KOing the bulkiest variants of Mega Scizor at +2 as well as 2HKOing Chansey and Blissey.
As you can see, basically special Toxicroak vs physical Toxicroak is pretty much like using special Lucario over physical Lucario, or vice versa, just that Lucario has higher offensive stats and speed, but Toxicroak's typing enable it to set up and get passed more Pokemon, such as Rotom-W and Keldeo.
Basically, all I wanted to say is that, Toxicroak can be a special sweeper, but in order to do so, you would have to edit your set and I would recommend you editing it into the one I posted above.