That's very strange – but also kinda good news 
The dependencies shouldn't make a difference (and the wheel should install everything it needs). The error you're seeing means that pip doesn't even acknowledge the file as valid, so you're not even getting to the install stage.
Which pip versions are you running in both envs? And if they're different, maybe try installing the same pip version your base env has in your new env? It could easily be some pip version weirdness.