I do not see what the problem with having a gun when there have been so many other examples of superior technology in the games. I think the hookshoot and clawshot are much more advanced than many modern small arms. Plus we have the many technologically advanced dungeons such as the Temple of Time. If they have classic grenades then the world of Hyrule is firmly in the age of the gun. I suppose Hyrule being a very high magic setting there could be arguments that guns are not developed or not as reliable as magical devices they already have. Especially when fire and ice arrows can just be given out to people for regular use. There is no real need to develop a small firearm when one can grant the ability to make fire arrows to someone so easily. Most of the time technological innovation comes from a need, or at least it spreads due to that need. It appers that Hyrule doe not have any real need for one so they do not appear alongside trains, bombs, sky canons, etc.
Now in many fantasy setting I am a huge fan of magitech. It is rarely seen in the Zelda series but has appeared many times throughout the Final Fantasy series. I would rather it not go to ridiculous things like giant mechs powered by magical energies, but simpler things like automated rooms and clockwork devices powered by magic I would have no problem with at all.
The only thing I see that might develop into a problem is that when most of these sword and sorcery games that include firearms, they are incredibly weak. Normally much much lower in overall damage than every bladed or melee weapon that game has. In many occasions a machine gun just cannot even compare to the level of might a hero with a trusty sword can dish out. (apparently video game developers know little to nothing of ballistics, they just think a small piece of lead is weaker than an arrow or a steel sword)
Gunners have very high Accuracy, rarely missing their targets. The downside is that Gunners do not deal as much damage as other Jobs,
http://finalfantasy.wikia.com/wiki/Gunner
So seeing many of the suggestions giveen here for something very low tech like a flintlock or matchlock with the disturbingly low rate of fire, it would possibly be the most useless item in the game. It might become another slingshot, only with a cooldown wait period before refire. Thinking about that, I would rather have another spinner take up space in an inventory, at least those can be fun alongside being useless for combat.
What I would have an issue with is almost any weapon replacing the sword as Link's main weapon. This would go beyond guns for me, a gun within the game I would not care about. But a gun replacing the Master sword or any other main sword as the premiere weapon Link uses I would not like at all. Things like axes, spears, etc, would not cut it for me. However I do not think that this is the topis of discussion, and even so I believe most people might hold the same opinion.