Based on the rules stated above, it appears you could use a bow that has been modified to manually (draw) launch an elongate paintbrush, with a specially modified color splash tip.

im also seeing nothing about non retention snares/traps, which are one sided, and instead of teeth, have modified paint sponges to mark the animal quickly and painlessly.

low velocity air guns, like say a potato launcher, or rubberband gun, can be modified to shoot color sponge "bullets". in fact any nerf gun might work well, soaked in paint.

i dont think you're out of options on this yet Mike.