A slightly different, and potentially easier way, is to use the component I designed and uploaded to the 3D Warehouse - https://3dwarehouse.sketchup.com/model/62d6ed17-eb0d-41c6-ba6f-371cc9e590ce/Kreg-pocket-hole-and-screws-30mm-38mm-and-52mm
[EDIT - see post #32 below for improved versions of this component, which has now been replaced on the 3D warehouse by a better one.]
Download the combined component Kreg Pocket Hole and Screws, and explode it.
Instead of trying to intersect faces, or actually remove the oval face, after inserting the hole, this component uses Cut Opening to merely make the oval transparent in the underlying wood component.
And the screws (of three common different lengths) are low poly heads, and 2D Face-Me threads, which keeps the edge and face count much lower than would a full 3D screw thread.
Easy to place, too. Open your ‘wood’ component for editing (double click on it, and if it has any, its parent component(s)) until you see the top or near face highlighting, then drag the Kreg Pocket Screw Hole component out of your Component Browser using the guide point at its origin, and place the guide point on the edge of the wood. The component also has Glue to Any Face set, so it will automatically align itself on the face you hover over before you click to fix its position.
Do the same for the screw. Use the Rotate tool to place it and the hole along the correct axis if the edge isn’t parallel to the green/Y axis or the blue/green plane.