I refuse this terrible term and invite everyone to use (following zitterbewegung's udemy link) to use "metacognitive skills" instead.
FWIW, I didn't interpret it as the polar opposite. I don't see that much of an issue with a model of skills as physical, cognitive, and emotional.
https://en.wikipedia.org/wiki/Meta
(Douglas Hofstdadter made a career of cheerfully pointing out that a theory about theories must include itself as the kind of theories it is about -- "I am a strange loop" and all that. But still, what the language means is that.)
Meta implies a hierarchy.
"Non-epistemic" might be an alternative to "non-cognitive".
I'm beginning to like "non-epistemic". Not everything about being a succesful intellectual or knowledge worker is about discovering the Truth.
"Metacognitive" has problems. My new favorite is "non-epistemic".