America is not a problem at all if the fight would be in the ring and PRIDE rules.
Cro Cop is kickboxer and he is much weaker in cage, altough he adapted some to unified rules at his older age.
Considering Mirko's resume, some people are forgetting, or newer fans do not know that Fujita and Herring for example were top 5 fighters when Cro Cop fought them, or that Randleman and Vovchanchyn were top 10 at the time.
Or that Magomedov, Waterman and Yoshida were top 15 then, like Nelson, Mitrione, Kongo or Struve are now, and that those were notable wins.
Cro Cop was also ranked LHW on Sakuraba fight.
Cro Cop beat the best wrestlers, UFC Champions like Barnett, Coleman, Randleman who were also NCAA wrestling champions. He beat Herring, Fujita, Sakuraba & Ron Waterman who is bascally a copy of Brock Lesnar. Mirko beat world wrestling champion Amir Aliakbari and 3 time American and Pan American wrestling champion King Mo. He beat WWE champ Del Rio and NJPW champ Nagata and also RINGS veterans Yamamoto & Kanehara.
So it is safe to assume tha Cro Cop would destroy Cormier in the ring, like he did all those other wrestlers.