Many combat-trained Wizards pick up secondary weapons in the event they find themselves unable to use their wands. Mechanical weapons, like other Muggle technology, tend to work very poorly in the hands of a Wizard. Most stick to archaic methods of defense: hand-to-hand, clubs, and bladed weapons like knives or swords. Why do you need a flamethrower when you can cast Incendio? Why grenades when a well-placed Reductor Curse will have the same effect? Weapons such as these will be automatically rejected. You may apply for artificed explosives but the application needs to be very good.

Wizards may apply to own and use guns, but keep in mind that guns flub up when they're in highly charged magical areas. They are prone to jam around Wizards casting spells and leaving magical residue everywhere. You may find yourself in the possession of a fairly useless club (remember that the wizards in POA actually thought a gun /was/ a club that Muggles used to kill each other with) - they probably fire accurately about 30% of the time. Remember that murder and assault are murder and assault whether you use a gun or a spell - using a gun instead of a wand will not keep you out of Azkaban, and the MLE may in fact throw in an "improper use of Muggle artifacts with intent to harm" charge.