We know that Voldemort knew that Grindelwald was not killed by Dumbledore, as he himself killed Grindelwald.
We also know that Voldemort knew that Dumbledore was the last person to wield the Elder Wand with its full allegiance because he killed Snape in an attempt to inherit that allegiance from him, who he assumed inherited it from Dumbledore.
Now Voldemort is no idiot.
Following this chain of logic, based off of what he knew, he must have realized that Dumbledore didn't gain the wand's allegiance through murder as he never killed Grindelwald, so why did he feel the need to kill Snape in order to win the wands allegiance for himself?
Surely he must have known that disarming him would have been enough. Was he so blinded by his desire for the wand that he was willing to try anything? Or was he so pressed for time that he didn't fully consider the matter?
I can't imagine the latter to be true as Voldemort himself said to Snape before killing him that he considered the matter for a long time, but that, of course, could be a lie.
Or perhaps he decided that what with Snape no longer being a competent spy after being outed that he had outlived his purpose and would be more valuable dead as a result of this last ditch effort to gain the wands true power.
I'm just answering my own question at this point, but I'd like to put it to you all. Is there something I am missing here? Is there any word from JKR that can clear up this seeming lapse in Voldemorts judgement?