The highest risk of chipping isn't with wood-grained moldings coated in clear coat, but rather with moldings painted in lacquer as original such as those used in earlier standard closed body types. Extra care is required in how far one goes and even when pushing down on the molding to relieve the pressure of the screw on the molding, you can never reverse course and go back even a tenth of a turn without chipping the paint. (Which for those of us who like to line up the slots in the heads is sometimes a temptation.

)
In other words, not a job to be done if you are in a hurry.
P.S. The extensive use of countersunk washers with the screws on the birch side panels for attaching the maple trim strips on station wagons has zero to do with minimizing chips in the varnish.