The wars of the 14th c.- 15th c. gave the Europeans a reason to work out how to make consistent , effective gunpowder, and by the end of the 15th c. small arms were reasonably accurate. How much hunting was done with matchlocks is an interesting question, however- they're not something that's easy for the hunter to keep ready to fire while waiting for a deer to run by, or for a bird to be flushed out of a bush. Wheel locks came into use after about 1509 ( possibly Leonardo da Vinci invented the mechanism circa 1500). They were more expensive, however, and matchlocks would continue to be employed by armies into mid-late 17th c.

There would also continue to be use of crossbows for hunting and target shooting into the 19th c. , using not only quarrels ( arrows) but stones. But for some kinds of hunting, guns had real advantages, like shooting at birds: a crossbow could not throw a cloud of small shot. Benvenuto Cellini would gleefully select the present of a fowling piece from the collection of Alessandro di Medici in 1535, while undertaking the job of designing and making a series of commemorative medals. Almost certainly that would have been a wheel lock, not a matchlock, as Cellini noted he selected the finest gun in the collection ( never humble, our Benvenuto). Rifles would have been available by then as well, and the Germans were making good ones in Nuremberg. But how much they were used for long-distance hunting of, say, deer in the mountains compared to crossbows I can't say. Certainly, they were used for target shooting, and lighter ones could have been used for hunting as well.

It's also the case that guns were gradually introduced onto the battlefield: there was no hard, fast date at which point crossbows were obsolete. However, a pretty good turning point was the battle of Pavia in 1525, in which small arms fire was very crucial for the Spanish vicotory. After Pavia, most European armies had some firearms, if they wanted to win.