Your pic does not show the extent of the problem or the surrounding conditions. That is to say, how much other stuff would you have to remove to recover the whole area? Or, could you apply a neat patch over the offending area?
Formica is generically called 'plastic laminate'; that is, it's made of layers of stuff with a top surface of colored material all impregnated with phenolic resin (unless it's the premium version that's uniformly colored throughout). You can sand the surface but not all that deep; you may have seen plastic laminate check-out counters in stores that are worn through the surface and into the underlying lamina. Sanding the surface will also change the sheen or surface pattern; it will also give a surface which will accept adhesive.
Thus you could apply a neat patch or recover the whole surface with matching plastic laminate. It seems likely to me that Mainship would have purchased their laminate already bonded to a plywood underlayment; if so, the bond will be pretty darned good and the laminate would not be removable. If Mainship laminated their own plywood components, they'd have their choice of adhesives and the removal might be easier. (Morgan used contact cement in our 1972 sailboat.)
Simply filling the holes you pictured might be the easiest w/o the bother of finding matching laminate. I think it would be appropriate, and easy, to countersink each hole enough to remove the ragged edge and any shattered material. Then apply the filler as neatly as you can. Subsequent sanding would unduly affect the surrounding laminate, even if it was the 'matte' finish.