You can definitely smoke cheese on a small offset. I started smoking cheese several years ago on my little Brinkmann offset.
I found it most convenient to arrange a few lit briquettes, like just six for example, next to each other in a 2x3 grid in the firebox and set one or two very small chunks of wood on top. The cooking chamber would not heat up much due to so little fuel, and the low burn temp of briqs helps too. The chamber would get smoke though.
Keep your temps below 80 or most cheeses can start to sweat, and that will affect quality.
Since it's getting towards summertime, pick a cool night, and start with only 3 or 4 briqs and see what temps you get.