The commonly available 5 minute or 1 hour epoxies are not really waterproof.
I'd say for just a few screw holes use JB weld. Epoxy must be painted over, it is not UV resistant.
Sometimes paint does not like to stick to epoxy, sand it and wipe it to remove any blush or shiny spots.
I use a lot of 2 part epoxy, of the type for laminating surfboards. To thicken this epoxy I use wood flour, which is basically sanding dust I collect in my belt sander from a 120 grit belt.
It turns the epoxy into various shades of brown depending on the wood the dust was colected from. One needs a lot more dust thean they would expect to use until the epoxy is about a peanut butter consistency. There are dozens of thixotropic agents one can add to epoxy to thicken it up, but wood flour/dust is free and more than effective enough for this task.
One other possibility is mixing the epoxy, then waiting on it to start thickening, and then once gooey and thicker, mush it into the holes with a straight edge, but this can get messy with stringy epoxy leaving hairs from cup and straight edge. One also needs to saturate the fibers with unthickened epoxy first.
If there is paint in the screw holes, I'd want that paint out of there first