The problem with making them unsearchable is that, when stacked on top of another body, you won't be able to search either.
The best solution in terms of gameplay, would be to have some sort of 'corpse selection' option, but I suspect that'd be exceedingly difficult to implement. Having the corpse disappear, on the other hand, seems like it'd be a good solution; so long as only the corpse that is empty is disappearing, and only if it's stacked on top of another.
Hey, if you think you can pull it off, by all means. It'd be a good addition.