The idea that private keys were in the hands of one individual alone is hard to believe just as Powell pointed out.
If the body is exhumed and it is identified as Cotton then still it does mean the end of the investigation. There will be an autopsy to check for clues how he died and since Mrs Cotton was the only person with him on that holiday and philanthropic trip the finger of suspicion will fall upon her even if the evidence might lack.
The other possibility is that if the body is exhumed and it is identified not to be Gerald Cotton then it opens up scope to widen the investigation. Mrs Cotton is not exactly out of this just yet and the plot could thicken even further.