Template doesn’t need to be clamped into place - pop some masking tape on the body and on the underside of the template, then use super glue, gorilla glue dots on the tape on the body - line it up, press it into place - it’s secure enough. Each side of tape is removed after, no residue or damage.
After chiselling, even the most carefullest of people will have an uneven contour, which will likely require sanding after to make good and properly flat, not to mention that to successfully remove the wall chiselled bit, you will have to eat into the floor just a tad to avoid splintering, and then the floor is slightly uneven. Hopefully the finish on the body won’t chip or crack in the process. If you don’t mind slight flaws in that system, then yep - nowt wrong with either, but the router will be cleaner and more precise with the caveat the template is correct.