If a wizard sells a second-hand wand, is this the same as winning it in a duel? Could Voldemort have bought the Elder Wand from Snape instead of killing him for it?
I'd hazard a guess at no, it wouldn't count.
Ollivander states that a conquered wand will usually bend.
"I took this wand from Draco Malfoy by force," said Harry. "Can I use it safely?"
"I think so. Subtle laws govern wand ownership, but the conquered wand will usually bend its will to its new master."
Harry Potter and the Deathly Hallows, chapter 24: "The Wandmaker"
And when Harry Potter uses Hermione Granger's blackthorn wand, which she willingly let him use, he has trouble with it.
The spider did not shrink. Harry looked down at the blackthorn wand. Every minor spell he had cast with it so far that day had seemed less powerful than those he had produced with his phoenix wand. The new one felt intrusively unfamiliar, like having somebody else’s hand sewn to the end of his arm.
Harry Potter and the Deathly Hallows, chapter 20: "Xenophilius Lovegood"
Selling a wand would probably also count as willingly given, and not conquered.
They should work well enough, but may have learned habits that are incompatible with their new owners.
It seems like willingly given wands, which would likely include a wand being sold secondhand, work about as well as wands won from their previous owner. He said using Draco’s wand, a wand he’d won from its owner, worked “at least as well as Hermione’s”. Therefore, Hermione’s wand, which she willingly lent him, worked about as well as a wand he’d won from its owner.
“Harry looked down at the hawthorn wand that had once belonged to Draco Malfoy. He had been surprised, but pleased, to discover that it worked for him at least as well as Hermione’s had done.”
- Harry Potter and the Deathly Hallows, Chapter 26 (Gringotts)
However, most wizards prefer a new wand to a secondhand wand, because a secondhand wand may have picked up habits from its previous owner that may not suit its new one.
“Most witches and wizards prefer a wand that has “chosen” them to any kind of secondhand wand, precisely because the latter is likely to have learned habits from its previous owner that might not be compatible with the new user’s style of magic.”
- The Tales of Beedle the Bard
Therefore, it seems likely that a purchased secondhand wand will work well enough for its new owner, but wizards are better off having a new wand that chose them instead of one that had been previously owned by anyone else, whether won from them or bought.