Elizabeth,
frankly, if it is was me, concerned with hand production rather than hand craft I would use Photozz's idea of the Dremel but not with a rotory saw or abrasive disk bit but a Zip bit. I like the idea of a die, but only if it used as a square jig.The jig would secure the lid and have a built-in square pattern so your shape could be cut out like a router pattern. Each lid would take under 30 seconds.
Otherwise I would talk to Steve P. ask him to program the CNC router to cut the square, make a jig to do 4 at a time and cut with carbide machine tooling.
My choice of method and technique, like most cases of production, are determined by the level of skill at hand (unintended pun) versus fit and finish desired.
(I am still inclined with the chisel idea,-possibly used with a jig, because yes, it would deform the cut, but I would use that curl-over deformation, for a tight fit around the light, also I would make separate round gaskets for each lid with an undersize square hole placed under the lid.If this light would be used outdoors this gasket it wood keep condensation from forming inside, and keep water, dust, and bugs out. for me it would be satisfying pro-touch.)