I just replaced some screws on the outside of my scamp
that had rusted. I figured that Stainless would be the way to go and instead of using the caps I just put some sealer around the hole before putting the screw in. I would take one of the old screws to a hardware store and tell them what you need it for and they should help you out.
Also, the screws I got are sainless #8 pan screws (You will want to get a length that matches what you had before) with the head painted white. These are pretty common at an old school HW store.