In story, there was only a few minute or so between the making of the unbreakable vow (which did require Harry to have his wand) and Harry using it to kill the Death Eaters. Voldemort makes the "You have 1 minute to tell me your secrets or you die" offer immediately after the vow, after all.

Not so. At T-20 seconds, Harry starts verbally stalling while he keeps working on the transfiguration.

It also would have shown weakness in front of the Death Eaters.

After he's already given them lengthy and detailed instructions about all the many different kinds of spell they must be ready to cast at this naked 11-year old boy at the first sign of trouble?

And Voldemort probably couldn't imagine anything Harry could have done. He's way too young for any really dangerous magic, despite his skill. Voldemort doesn't know about nano-wires and all that stuff. It's probably unimaginable for him that so little magic could have such a big effect.

He knows that the Harry is a walking extinction event waiting to happen, and that Harry knows secrets powerful enough to be worth learning (potentially even powerful enough to end him - cf. "power he knows not"). Indeed, these are the two facts motivating his actions immediately prior to his defeat.

If he had demanded that Harry drop his wand, and Harry had refused, he would have been forced to kill him without learning any of his secrets.

Why? Surely at least one of his Death Eaters knows Expelliarmus.