If by colloquial, you mean "slang" the answer is no. If by colloquial you mean common vocabulary, both "feat" and "skill" are ordinary English nouns.
Feat refers to an accomplishment. Climbing a mountain, is a "feat". Any kind of final accomplishment is a "feat". Graduating from a school is a "feat". Finishing a test is a "feat".
Talking to a stranger may be a "feat," suggesting that it was difficult for you to do.
Speaking in front of other people can be a "feat" if it was a frightening thing for you to do.
If you drank a lot of alcohol, it might be a "feat" just to put your socks on in the morning.
Skill is an ability. I have some skills. I can shoot a Traditional Longbow.
I can play chess. I am a fly-fisherman. I hunt pheasants with a shotgun.
These are all acts of some skill.
I can ride a bicycle. I can review books. I can teach the basics of English language.
I can prepare meals. These are all skills that I possess.
I am a good public speaker. I can sing; but I cannot dance.
I can debate. I know how to research almost any subject. These are all basic forms of "skill".