As noted above you can use water based paints if you take some care and the extra step of weighing the parts down while they dry. I build HO scale model rr kits that use the same thin plywood and even thinner veneer pieces to build up the models. My preference is to use solvent based paints as I find it very easy to control the paint density and high light rather then obscure the detail as I paint. At times some pieces will warp but I have found the warps fairly easy to remove by some judicious bending in the opposite direction. As you noted the pieces are plywood so it is rare that something will break while you do this.
If you want to see an example of an HO kit, I am currently doing a small blog in the RR forum titled “East Shops Tower on the Buffalo Western”. East Shops Tower on the Buffalo Western