In our last place we had a cat flap put into a glazed french door. That involved getting new sealed unit built to spec. It wasn't cheap but wasn't massively expensive (I think about £250 about a decade ago, and this was a full door-sized unit). I was very happy with it, no problems in the six years we lived there. It has to be cut properly though.
I'm not sure really why any approach would affect insurance or security, it's not like any pane of glass can't be very easily smashed and burglars are unlikely to fit through a cat-flap shaped hole (unless they are quite literally cat burglars, of course), as I learned recently (gardener with strimmer vs. patio door, one small stone made short work of a pane of toughened glass).