I've been reading a bit about wandlore and Harry's ownership of the Elder Wand. Reading about how Harry got it and other rules for ownership of the Elder Wand got me thinking. Yes, Harry understood that Draco earned the wand from Dumbledore, and not Snape who killed him. Yet, it had been almost a full year since ownership transferred to Draco, so how did Harry know that the Elder Wand's master was still Draco Malfoy? He could have lost ownership to anyone else he dueled, fought, or otherwise lost to. I understand that this may not have a canonical answer, but I would prefer one if it exists.
We also must consider the likelihood of Draco having been in a position where he might have been disarmed (before Harry did so). Draco Malfoy wasn't the kind of Death Eater Voldemort would send to fight against other wizards. We know he couldn't get himself to kill Dumbledore, and he also hesitated before confirming Harry's identity to Lucius and Bellatrix. Which means he might have been having second thoughts about which side he was on and Voldemort was smart enough to have figured out Draco would be useless as a tool to inflict terror upon the nation.
Even if Voldemort hadn't figured that out, we know Lucius and Narcissa care about him deeply, and would have done anything in their power to ensure Draco wasn't sent out on Death Eater missions (where he might have been in a position to be disarmed). I think we can safely assume he was living in relative peace and comfort at the Malfoy Manor till Harry was brought there, and that Harry was the first to have disarm him since he disarmed Dumbledore.
Obviously, Harry didn't realize he was the true owner of the Elder Wand during his final duel with Voldemort. He had given it some thought before coming to the conclusion. The fact that Draco hadn't been disarmed by anyone prior to him was an assumption he made, but a safe one. Not to mention that was probably the only thing that would have saved Harry. As good a wizard as he was, he was still no match for Voldemort in terms of magical skill and power.
So yes, it was a shot in the dark, which could have backfired, but it wasn't a shot in complete darkness and it was a shot Harry had to take.
After Harry returns from 'King's Cross' station, Voldemort performs the Cruciactus Curse on Harry to make sure he's dead. But at that point Harry feels no pain because the Elder Wand wouldn't hurt him, its master. I think that's how Harry confirms that he is the owner of the wand and thus, proves that no one else had disarmed or defeated Draco in the past year. Hope that makes sense.
The way I see it, it didn't really matter. You are right that Harry had no way of knowing whether Draco (who Harry knows gets into lots of fights) still had mastery of the Wand, but there was a more important point to get across. Here is what he says about the wand:
"Severus Snape was never the true master of the Elder Wand. He never defeated Dumbledore."
"Aren't you listening? Snape never beat Dumbledore! Dumbledore's death was planned between them!"
"You still don't get it, Riddle, do you? Possessing the Wand isn't enough. Holding it, using it, doesn't make it really yours. Didn't you listen to Ollivander? The wand chooses the wizard... The Elder Wand recognized a new master before Dumbledore died..."
Harry stressed the point that Voldemort was not the master of the Elder Wand. It was lucky for him that he was, and a good coincedence. He had no way of knowing if he was the master, he just knew, and communicated, that Voldemort was not.
Because Draco's own wand worked for Harry.
This meant that when Harry beat Draco, he must have won the allegiance of Draco's hawthorn wand. Thus, just before Harry beat Draco, Draco had the allegiance of his own wand, which means nobody had defeated him before Harry came along.
If nobody had defeated Draco, then nobody could have won any of Draco's wands--not the hawthorn wand, and not the Elder Wand, either. Because the hawthorn wand now works for Harry, the Elder Wand should, too. If someone else had defeated Draco and won the allegiance of the Elder Wand prior to the incident at Malfoy Manor, that person would probably have won the allegiance of Draco's wand as well. But nobody did until Harry, so Harry must have been the first.
Note that this logic is not entirely flawless, since we know that the Elder Wand is much more volatile to a switch in allegiance than most wands tend to be. As ʀᴇᴅ_ᴅᴇᴠɪʟ226 puts it in his answer, however, it was a safe enough assumption, at least from Harry's point of view.