I’d have to experiment a little, but was thinking just a 3/4” frame, a bit longer than the table width with an opening in the frame that would allow you to see what your doing, but still give good support to the router base. If for example the opening is two inches wide (really just depends on the size of your router base), clamp it down, do a 2 inch area, then move it, do two more inches, etc. Not the quickest, but would get the job done.
If you have a router guide, use the guide against the outside of the table edge and do the perimeter of the veneer first.
Set the router depth to the thickness of the new veneer, plus the frame thickness, plus a hair deeper.