OUCH! Is there any other way? Once drilled always drilled. Suction mounts? Pole mount? I just hate to think about seeing clear-coat, glitter, and fiberglass turn to white power on a new boat. But it's your boat and you need it to work for you. Still I would drill at last resort. even to the extent of having mounts placed into the boat to match the surrounding area. Screws in fiberglass have a tendency to wiggle loose over time and moisture leaking through to areas it don't belong, or pulling out leaving flakes broke around them.
If you must drill, put masking tape over the area you are drilling and use a sharp high speed drill. and use a bolt washer and non loosening nut with a dab of two part epoxy around the hole.