Abbots has some nice spread sheets

I think modeling the skin as a thin cylinder is problematic. The part of the skin contributing most to bending resistance is the thickest part of the wing, because it is furthest from the common centroid. That part is pretty flat. All those cylinder calculations get pretty wonky if the shell is not a perfect cylinder. So I will just model it as a bunch of small slices.

Anyway the critical sigma is pi^2KE/12(1-0.09)*(t/b)^2

b (loaded edge length) is a bit arbitrary,as some of it is in front of the spar (18"), while some of it is behind the spar (21") and some of it is stuck down hard to the spar caps and truss ribs going over the spar (which will not buckle at all).

In any event,

K (buckling constant which varies with aspect ratio of panel) is >14, possibly much greater, as the aspect ratio is very small with a free span along the load direction of 5.5" and a panel width along the chord of 20" (b-if we take the part that contributes the most to the second moment of inertia).

E is 557k

t is 0.102

b is maybe the middle 20" of the chord of the top skin

So you get something on the order of 150psi for critical buckling stress.

Taking the 20" x t is 2.04sq in, times the 150 is about 300 pounds before it buckles

Plus the little bit of skin that stays in axial compression atop the spar itself; that acts sort of like a mini spar cap. The caps are interruped by the ribs, so not contributing much except to space the skin out away from the spar 0.25" and hold the skin in column.

Anyway I will have to put this stuff into the spreadsheet with the spar calcs and see how far it goes loadwise before it hits 150psi in the top skin.

After that it deflects, but still contributes because deflection is less than elastic limit.

Almost this is very similar to what the OP should do for their wing. I will say that 1/8 ply should resist buckling well but that it depends quite a lot in the rib spacing, which defines the panel size. Also, start with the spar calcs because if the spar holds your target load then you can be pretty confident that the skin will add quite a bit.