The Snipers I have talked to go with either a MK23 pistol, or a Mark-I.
These are two guns are both very quiet out of the box, which is why snipers seem to like them. Both shoot decent and with a little money, both can be upgraded to be quite amazing sidearms.
When talking about SMG's, for snipers, I have seen guys run the gambit from MP9, MP7, MP5, very small M4's, a few shotguns, and a few M4's.
In my opinion, the reality is, if you are running a sniper riffle, and you need a backup weapon, one of two things have gone wrong, Either you aren't great at being sneaky
yet and need to
hone those skills or they got lucky and walked up on you while you were making a good stalk.
So lets take a look at some tactics / choices;
Option one: An SMG is gong to alert more people to your presence, with the sound of the gun, the rate of fire, and the dead guys yelling hit, it's all going to make it more difficult to stay concealed or get re-concealed before more guys come looking to see what has happened. So although going loud is an option, you're probably going to end up getting hunted and dying on the run. Not a great option in my opinion.
Option two: You are on a good stalk, and you get walked up on, and they find you. You can try to kill with quiet accuracy and then disappear into the bush, displace knowing they are going to come looking for you with their friends, but you will make sure they won't find you the next time. Then when things settle down, resume you original hunt.
Option three: You are on a good stalk, and you get walked up on, you stay on target, stay concealed, and stay quiet, let them pass, and continue your hunt.
Here's another way of looking at it when purchasing a secondary as a sniper there are a few things to consider about the gun.
Overall Weapon size, the bigger the secondary weapon, the longer it's going to take you to get that weapon on target. If it's an M4, you will most likely have it strapped to your back, you will need a considerable amount of time to get that weapon off your back and onto you're shoulder ready to shoot. If it's a pistol, it will come to a firing position faster, but where and how do you carry it without it taking a beating while you are crawling around in the bush.
Magazine size, you are probably going to want more than one magazine for you're weapon, especially if it whole purpose is a S.H.T.F. weapon, so magazine size and shape need to be a consideration, if you are carrying an extra mag or two on your body as you move through the bush, the smaller the better so it doesn't snag on stuff or get in your way when you are lying prone trying to use your primary.
Lastly how am I going to carry this? I see a lot of new guy stuff it in a backpack, tote it around about 1/10th of the day before realizing they will never have the time to take the bag off their back, take the weapon out of their bag, and get the weapon ready to fire, before getting taken out by the enemy and carrying it around all day like this is fruitless so they drop it at spawn... Like I suggested an M4 will most likely be strapped to your back it can still be cumbersome, but accessible. Shotguns, have scabbards, again accessible, but cumbersome to draw, Most SMG's are too big to fit in a holster, and if you find a holster that fit's it, it's still going to be floppy on your equipment. And like a touched on before Pistols are great in size, but can be difficult to find a safe place for them to live while you move around.
Finally just a note about snipers in general. Realize that Snipers in Airsoft as in the real world are tools to be used for a specific purpose. Many events will not have commanders who are assigning specific targets to specific units or roles. These events are your chance to practice your field craft, figure out how to move quietly, how to get behind enemy lines, how to stay concealed, and how to properly choose "targets of opportunity", how to be an effective sniper and an effective member for your team. This way when you get to an event where there is a commander who needs a sniper to take out a specific target or hold over watch on a specific AO, You are ready to move into position without being seen even if that position is behind enemy lines, you are ready to take out targets of opportunity, or stay on target and eliminate a specific target, you are there to hunt, and you are ready to disappear back into the bush once you have completed your mission, radio it in and are already in a good position for another tasking.
Alright back to the guns... Links
The Mark - I
https://www.evike.com/products/24078/The MK23
Several brands make a version of this gun, TM / STTI / Y&P / ASG as well as a few others.
You are looking for the non-blow back or NBB version on the MK23 (that's why it's so quiet) The different brands have their ups and downs, and I'll let you do your own research because it's all based on price point, and availability.
That's my 2 cents, take it or leave it, hope it helps.