There are 2 distinct questions here:
1) Is wearing shorts chukas hagoyim?
2) Is it tznius?
I don’t know what constitutes chukas hagoyim so I can’t comment on that but I do know that my Rebbeim hold that wearing shorts in public is not b’geder hatznius. In a private setting, even a very public type of private setting such as a camp, this may be different even if there are women around. But, they are definitely very against wearing shorts on the streets of NY, even if you are exercising. In the gym is another story, but on the way to the gym, wear long pants.