I'd keep it, and have like fifty replicas made. I'd then proceed to snap it about three times, give it to a dozen people, and have it taken from me by half a dozen more, all the while explaining conflicting accounts of the "real" story to a hundred different people and reporters.
The replicas would be completely functional wands on their own, and I'd keep one of them in a hidden pouch in my robes while using my ordinary wand for everything else. That way, if something turns up I can hand over the elder wand without actually giving it up, and continue to elaborate the confusing mess of nonsense surrounding the wand so that nobody has any idea who really has it any more.
The real elder wand would just be sitting in a vault at Gringotts for when something turns up that I actually need it for.
