Here is the full range of weapons that your 4 armed friends would reasonably have:
Better than your hands, but not by much. Easy to make, use and conceal. If each arm is less strong then lighter weapons for each hand might be better.
You will be able to have one handed, two handed, three handed, and four handed swords. Since each individual hand is less powerful, you are likely to not have swords much bigger than our swords. However, the hilts will be larger.
Shields again will be used like normal in most cases. As I will show later, the shield might be modified to also handle simultaneous use of long arms in addition to pistols. However, pre guns shields will be bigger since the two handed sword can get around the shield better.
SWAT members might also use the load out below to get the most "tactical" load out. Shield, long arm and pistol. Shield for defense, long arm for long range attacks, pistol for reloading and close up attacks.
If your creatures are less strong in each individual arm, their pistols will be weaker. While crazy things like Dessert Eagles might not be possible, nearly any other small arm would be reasonable. Revolvers and other weapons would also make sense. These weapons exist because they are easy to make, easy to smuggle, concealable, and good for hunting or self defense.
- One sided long arms
Since two handed weapons don't have to be fired with a left and a right hand, there will be an opportunity to fire weapons with only one side of the body. This will let the user either carry a shield on one side or expose even less of their body when going around a corner. In the case of shield this means that your gun grip will have either a normal grip or a fixed canted grip to the user's dominant side, as seen below. In the case of the less exposure on corners, your grip will have a lock that can be adjusted on the fly to let the user go either left or right around a corner. These grips already exist in real life, but are uncommon, in your universe they will be very common.
Each of the examples below has a straight grip, and then the canted grip.
- Long Range Rifles
For long range rifles, bipods will be more stable than hands, so there will be no change. For bolt action rifles meant to be used in a standing position either extra grips or people will just grip in the appropriate positions. because Rifles are longer on average there will be plenty of space to grab the weapon. Bolt action rifles will be very common and well used by these aliens since they can keep one hand on the bolt while aiming and work it with out taking their hands off their gun.
Since shotguns are not accurate and rely on the shoulder to absorb recoil, shot guns will remain mostly unchanged if they are meant for all four hands.
- Various Heavy Weapons
Anti tank weapons, large machine guns, grenade launchers, and mines will remain unchanged. These don't depend on the number of arms, but more arms can stabilize the weapon, or can brace themselves with two hands while firing.
- Under Barrel Weapons
The one really cool weapon that could be done is under barrel weapons, or other combination weapons. These are smaller weapons attached to larger weapons, these would be under barrel shotguns, or grenade launchers. Normally these are sub par because you can't reload your second weapon while you have two hands on your weapon, meaning you might as well put down your first weapon while reloading. but since you have four hands you can afford to use two hands to reload your second weapon, as you hold your first weapon.
- Two Weapons
Since you can reload a weapon with two hands while you hold another with two hands this means you can shoot two guns. Not at the same time, but as you get close to running out of one gun you pick up another and aim that while reloading the first gun.
- Corner Shot
The weapon you have described bears resemblance to a corner shot weapon. This isn't necessarily a two handed weapon, or a more than two handed weapon, but having two hands to steady, one to pull the trigger, and one to aim would help. This takes your ability to turn corners better than other species to a whole new level since you now don't even need to be around a corner to shoot them.