You can mask around the holes by using a small single hole punch to punch a hole in the masking tape, then put that hole over the hole you are filling, and put a piece of tape on the back of the hole you are filling. Now you can use a thin filler in a syringe, and just drop it right in. If you have a steady hand you can put the tip of the syringe on the hole and inject a tiny dab in the hole. Just don't use a lot of pressure or it will squirt out the back. Any mess will be limited to the area of the hole in the masking tape. Sanding will be minimal, and it will take no time to fill them this way.

-Malcolm