Cavity wall insulation brick replacement
My understanding is that the insulation is stuck together with some kind of resin so it won't just fall out. I've seen one house where small polystyrene beads had "leaked out" around a poorly sealed vent, presumably during installation, and had then solidified into a sort of large drop shape. Presumably this depends on the exact type on insulation. The British National Insulation Association (I'd never heard of them either) mention two types of cavity wall insulation: blown mineral wool and expanded polystyrene beads. Mineral wool is fibrous and sticks to itself so is unlikely to be a problem. Regarding the EPS beads, they say:


  The polystyrene used for [cavity wall insulation] is in the form of virgin pre-formed bead which is usually combined with a binding agent or adhesive at the time of injection.


Removing the brick shouldn't be too hard with a grinder. After cutting out the mortar, you could drill a couple of holes, insert some plugs and screw some chunky screws in to be able to pull the whole brick out.

You can get mortar guns to push mortar in around bricks. Never used one myself but they should help you do a good job in a situation like this.