I think that for CaP4, the idea of hard counters on top of the hazard weakness and relative low base power of STAB's available. However, I think identifying a list of Pokemon who should retain the ability to destroy CaP4, but risk getting destroyed by the right move on the switch is more important. This makes the Pokemon much more viable, as it means it can sweep under the right circumstances, but risks a number of Pokemon coming in and destroying it if it misplays or does not have the right move in its set to deal with its checks.
As such, I would like to propose Tornados-T, Infernape, Terrakion, and possibly Volcarona as its situational checks.
Infernape and Terrakion are taken care of by moderately powerful STAB moves, but I think that leaving CaP4 with the ability to be situationally checked by these Pokemon is important, as these are among the fastest Pokemon with Super Effective STAB that could potentially revenge kill CaP4. This leads to a very interesting dynamic where CaP4 will have to take risks on the possibility that the other side comes in. This makes CaP4 inherently risky, and I do not believe it should have reliable ways to make these two Pokemon a complete non-issue.
Tornados-T is similar, in that I believe it should be threatened when coming in, but still be able to attack back. Tornados-T is something of a staple in the current OU metagame, and being weak to it is a major risk. However, I believe that CaP4 should still have the ability to hit it back, bringing it into the same situation as Terrak and Infernape.
Volcarona and Genesect are in a similar vein. I believe they should be threatening if they get in, but CaP4 should have means to deter them from entering play. Of course, it will be hard pressed to run moves to destroy all of these diverse checks in one set, so it may have to bluffs and other means of psychological warfare, or ensure that these checks are all destroyed before CaP4 begins to do its work.
The problem with the "Pokemon who can kill after switch in" method is that any team with two checks will make it hard for CaP4 to score more than one kill if it has to switch into hazards. This means that spin support and clever play in an attempt to destroy at least all but one of the checks to CaP4 on the other team. This makes it a risk in and of itself to have on the team. But this also means that I strongly oppose any Purusit users (Tyranitar, Scizor... does anything else actually use it in OU?) from stopping CaP4, as that would mean that they would almost prevent it from being viable as it could likely only score one kill per match- a reward hardly worth the risk. In fact, Scizor and Tyranitar should be afraid to switch in even after a revenge kill if this Pokemon is going to succeed.