In a slip or skid, how does one wing have a higher angle of attack and more lift?
You are mostly correct, but the fuselage distorts the airflow in sideslip such that the windward wing sees a higher angle of attack near the root, and the leeward wing a lower angle of attack. Please see the drawing below for an explanation.



The blue lines show the sideward component of air flow and the red arrows the resulting rolling moment.

This is why low wing airplanes need more dihedral, and high wing planes like your 172 almost none. Wing sweep adds more directional stability, and then you even find aircraft with pronounced anhedral, like the Harrier jump jet or the F-104 Starfighter. See this answer for more detail on this.