I agree that Surface Skimmers shouldn't increase oxygenation much, BUT, with my XP3 filter, air does buildup and get expelled regularly since using the surface skimmer. I'd bet, but can't prove, that the regular expelling of air bubbles helps.
More reliable alternatives are to have your outflow agitate surface a little, though this will outgas CO2, or as jarthel said, put a pump and airstone on timer to run at night. That's what I do...a SMALL pump running an airstone when the lights go out.
Here's the bigger question. I do it because it seems to make sense and has no downside. I have no indication that I NEED more O2 in the water column. Why do you think you do and with what urgency?