you will be fine. I did this to my old trap 12 years ago. back then, they only gave you the molding, nothing about screwing it on. After it came apart a few times I added the screws myself.
For the Pro I just got, I used thier screws. I would drill pilot holes with a small drill bit first. Those screws are fine, the molding as a metal reinforcement in it, they wont go anyplace.