If you take your fender tag off and put it someplace for safe keeping, there is probably a better chance that it will get lost at some point, or if something happens to you sometime and your family has to sell your car, they won't know about the original tag, then there is of the tag being stolen at a show.
Better to replace one of the screws for your original tag with a screw with a nut so that it would be difficult for someone to steal. Or use some JB Weld or epoxy or something for that purpose. Anyone who would steal a tag would only do it if they could remove it in a few seconds with a screwdriver.