…But the most likely (far from perfect) answer, is that you are partly right. Harry was taking a risk, but not as big a risk as you made out. For if you consider what Harry knows about wands at this point, it is a fair, if not foolproof, assumption.
What we, the reader, and therefore Harry, know when formulating this plan is that wands are not simply blunt catch-all magical tools. There is a deeper component to the wizard/wand relationship, which is one of the first things we find out about magic in the entire series (with Harry’s wand troubles in the first book, if you need the reference). When Harry ‘takes a train’ to face Voldermort, he knows a few key things about wands. Firstly, that there is a bond forged between a wizard and a wand. This bond does not respect time or space, or indeed physical boundaries. And as Harry finds out when he takes multiple wands, they all work. So your question assumes that it is obvious that this should only logically apply to those taken by hand. But what Harry assumes is that it is toileh on the gavra, not the cheifetz. Now, this would be a very brave (read: stupid) assumption to make about an ordinary wand. But what Harry is gleaning knowledge about is the Elder Wand. And the Elder Wand passes on through defeating the previous owner, and therefore from Malfoy. With the Elder Wand it is a much fairer assumption, seeing how it passes on through duels. So defeating him in any context should work.