If you can keep your pit temp super low, and use a very gentle source of smoke.... your smoke times will be between 2 and 6 hours. It's best to sample small slivers along the way to determine the flavor you like best.
You might look into the tin can and soldering iron method, or try lighting one briquette and adding some chips around that. You can even consider putting a tray of ice cubes below the rack where the cheese is, this will cool down the smoke.
I would try two kinds first.... cheddar and pepper jack. This will give you a broad range of back flavor to go with the smoke flavor you will add. I have tried many, many brands and my current favorite is Tillamook. I prefer the extra sharp cheddar (black label) in either the white or yellow, it's about $3 more per brick than their regular cheddar, but worth it.
I have found that Colby won't take smoke as easily as cheddar or jack. I'm not a big fan of smoked swiss, but I do smoke some for friends. Most of the soft cheeses come out good, you just have to watch the temp. And speaking of temp, you can always smoke it for an hour, move to the fridge for a couple of hours, then return to the smoker....
Try and find a grate screen to set your cheeses on, or you can lay out cheese cloth on your grate too.
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