I'm looking for an expression that conveys an excessive risk management approach that ends up having a worse effect than what it is trying to protect against.
A common saying that comes to mind is The cure is worse than the disease, which thefreedictionary says first appeared in Philip Massinger's 1624 play The Bondman.
Cutting off the nose to spite the face" is an expression used to describe a needlessly self-destructive over-reaction to a problem.
Sounds like a good fit to me!
I agree with @FumbleFingers for the general case; "the cure is worse than the disease" is well-understood. If you're looking for something a little more colorful (akin to your title), "we had to burn the village in order to save it" is a US expression arising from the Vietnam war. (As noted there, this is not the original formulation, but it's a common version.)
I'd say you're throwing the baby out with the bathwater, in that you're accomplishing your goal but doing it in such an overly thorough way that you end up with very negative consequences.
The phrase "don't burn down the barn to kill the rats" was used to criticize McCarthyism.
Militarily speaking, the doctrine of mutually assured destruction (MAD), might fit this bill:
A doctrine of military strategy and national security policy in which a full-scale use of high-yield weapons of mass destruction by two opposing sides would effectively result in the complete, utter and irrevocable annihilation of both the attacker and the defender, becoming thus a war that has no victory nor any armistice but only effective reciprocal destruction.
EDIT: In deference to @Mitch's comment below (and the two flaggers), I've hyperlinked the word Pyrrhic, for the record. Thanks, Mitch.
There is a German word "Verschlimmbesserung" which I've seen used in English literature (without it being translated).
Literally translated this would be "disimprovement", ie. an attempt at improvement which makes the end result worse. I think this might fit what you're trying to say.