I would say it really depends on the wand, since each wand has it's own unique but somewhat predictable identity that is based on the woods and cores (dragon heartstring is more willing to switch allegiances than phoenix and unicorn, the former being the most difficult to form a bond, but more loyal once formed and the latter being more willing to form a bond, but mid in the loyalty once bonded.).
No mention of what happens if a wizard chooses to use a new wand over the old. Presumably the old wand is still bonded to you and would work just as well as the new wand (since allegiance can be switched if defeated in combat, there would be a number of duelists who would be constantly swapping wands if the allegiance of one meant the disloyalty of the other.).
It also bears repeating that the Elder Wand is famously fleeting in loyalty and it's unique make of Elder wood and Thestral hair core combine two wand making materials that already produce a more willingness to break disloyalty (Thestral Hair was not favored by the Ollivanders because this made it a lesser core material.). Voldemort's wand being of a Phoenix Feather core would likely not have waivered, since they tend to make very loyal wands by any stretch. We also see that Voldemort was able to use another wand that was not his (Mr. Malfoys) just fine, without any difficulty and return to using his own (he knew he was going up against Harry and was trying to prevent the twinning effect from their last encounter from being an issue.).
Similarly, Harry was able to use Draco's wand for much of the Final Fight, but after making repairs to his own wand went back to using that without issue in his adult life.
I would say it really depends on the wand, since each wand has it's own unique but somewhat predictable identity that is based on the woods and cores (dragon heartstring is more willing to switch allegiances than phoenix and unicorn, the former being the most difficult to form a bond, but more loyal once formed and the latter being more willing to form a bond, but mid in the loyalty once bonded.). No mention of what happens if a wizard chooses to use a new wand over the old. Presumably the old wand is still bonded to you and would work just as well as the new wand (since allegiance can be switched if defeated in combat, there would be a number of duelists who would be constantly swapping wands if the allegiance of one meant the disloyalty of the other.). It also bears repeating that the Elder Wand is famously fleeting in loyalty and it's unique make of Elder wood and Thestral hair core combine two wand making materials that already produce a more willingness to break disloyalty (Thestral Hair was not favored by the Ollivanders because this made it a lesser core material.). Voldemort's wand being of a Phoenix Feather core would likely not have waivered, since they tend to make very loyal wands by any stretch. We also see that Voldemort was able to use another wand that was not his (Mr. Malfoys) just fine, without any difficulty and return to using his own (he knew he was going up against Harry and was trying to prevent the twinning effect from their last encounter from being an issue.). Similarly, Harry was able to use Draco's wand for much of the Final Fight, but after making repairs to his own wand went back to using that without issue in his adult life.