I would remove the existing medicine cabinet to see what is behind it. Mine is only secured by two small screws on each side. Easy to remove. There are lots of ways to secure the new cabinet to the wall, and it doesn't take much strength to make it secure. You may even be able to use drywall anchors through the back of the cabinet, depending on what is on the wall behind the cabinet. My medicine cabinets have a sheet of drywall behind the cabinet with a dead space behind the drywall. But, you won't know what is possible until you remove the cabinet. Hopefully, you won't be storing gold bars in the medicine cabinet.
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