Sirius is another character whose wand is never revealed, and whichever one he used after his escape from Azkaban must have been one he stole, borrowed, or won by defeating its previous owner, because he could hardly walk into Ollivander’s and let a wand choose him. But what kind of wand would have chosen the younger Sirius Black?
I love the idea of Sirius using a dogwood wand, and not just because of his animagus form. Here’s what “Ollivander” has to say about dogwood:
Dogwood is one of my own personal favourites, and I have found that matching a dogwood wand with its ideal owner is always entertaining. Dogwood wands are quirky and mischievous; they have playful natures and insist upon partners who can provide them with scope for excitement and fun. It would be quite wrong, however, to deduce from this that dogwood wands are not capable of serious magic when called upon to do so; they have been known to perform outstanding spells under difficult conditions, and when paired with a suitably clever and ingenious witch or wizard, can produce dazzling enchantments. An interesting foible of many dogwood wands is that they refuse to perform non-verbal spells and they are often rather noisy.
Much like the Weasley twins, the younger Sirius Black was something of a prankster, his playful nature reflected in his animal form. However, like the dogwood wand, he was perfectly capable of being serious (no pun intended); he is one of the few from his family to choose not to pursue dark magic and follow Voldemort, instead joining the Order of the Phoenix shortly after leaving Hogwarts.
However, he could just as easily fit the description for red oak:
You will often hear the ignorant say that red oak is an infallible sign of its owner’s hot temper. In fact, the true match for a red oak wand is possessed of unusually fast reactions, making it a perfect duelling wand. Less common than English oak, I have found that its ideal master is light of touch, quick-witted and adaptable, often the creator of distinctive, trademark spells, and a good man or woman to have beside one in a fight. Red oak wands are, in my opinion, among the most handsome.
This fits him especially well as an adult, when his mischievous childhood persona had been eaten away by years in Azkaban and fighting in the war. The adult Sirius is certainly warm-hearted and has little regard for rules, but he’s grown up quite a bit. I think that instead of the “quirky and mischievous” dogwood, the Sirius we meet in the present day might have favored something more like red oak if he had the chance to be chosen by a wand.
For the core, my first instinct is dragon heartstring, which produces the flashiest magic, but phoenix feather is also a possibility, for its independence and spontaneity.