Someone else on this forum mentioned that they used a spray foam, and they drilled holes through the sides and bottom of the fridge from the inside, and through which the spray foam was then squirted. Finally they fitted those white plastic caps, that you get with self assembly furniture to cover the ends of screws, into the holes and that was it, job done, and an inside job at that !
Much simpler than pulling the furniture apart, and for which my advice would be - Don't.