Ok, you asked...
Let me preface this by stating I'm no expert at smoking cheese. I've only been doing it for about 40 years. Please take my comments as ideas rather than gospel.
1st of all, that smoke box on the side of yer smoker is of little use for 'cold' smoking anything. It's bolted onto your grill and will achieve grill temp in short order.
One cannot hot smoke cheese. Cheese (depending) will start to sweat at 90 degrees F. If you hit that mark after a couple hrs, you'd be ok. If you hit it in 30-60 minutes, you wasted your time.
I have a bottom dwelling Traeger Jr. It will smoke all day long at 120-180 deg, ambient temp depending. As you can see, those temps are far above the sweat point of most cheeses that would benefit from smoking. Sure, you could throw a brick of parmesan in there and be ok as its a hard cheese with little moisture. What you would gain is a bitter tasting outer layer. The inverse is trying to smoke a soft cheese. Forget I even mentioned that.
I'm a cheeseaholic, and about the only one I never tried is the one with maggots crawling about it inside.
Back to topic...
Most firm/semi-firm cheeses can benefit from a cold smoke if that's yer choice. I'm a fan Of WSU Cougar cheeses. They come in a 22 oz can. Yes... a can.
I'd not smoke the Cougar Gold as it's too good as is. Many other varieties, I smoke at will with very good success.
The fact that just about all pellet smokers just can't operate at the temps required, means you have but a few choices.
Many smokers have a 'chimney'. They look cute I guess, but really don't serve any useful purpose other than being the exhaust. Should you have one, you'd need to adapt it to a hose that ran 10' or so away from the smoker. Doing so would help cool the smoke. My Jr has ports on the back so this is not an option.
The most useful option is smoke tube/pan/gadget that allows you to use pellets without turning on the fire of the grill. Yes, it's dirty smoke. Some have adapted their pits to limit fan flow without engaging the heat. The fan may blow, but it's still dirty smoke. So why bother? The only advantage I see would be if you added a pan of ice to the rack and thereby keep the temp lower than ambient. For a bit.
I smoke my cheeses when it's COLD outside. A 10" tube will raise the temp from 32 to 100 in a couple hours, so I'm diligent in the process.
After smoking, I pat off the sweat if there is any, and let sit overnite in the fridge lightly draped with plastic wrap. The next day, I vacuum seal and let rest for 3-4 weeks. You can then freeze if you like, but my cheeses will easily last 12 months in the fridge.
I'm tired now....