I'd remove any dead foliage, unearth the tubers, clean them off by removing any clumps of soil, and put them in a cool, dry, dark spot. Without growing medium, light, or water, new growth will come to a halt. Hopefully, these conditions will induce dormancy.

Cannas are left in the ground in my zone, but I'm sure someone here can tell you the best way to store cannas over the winter. You can cut them down and dig up the rhyzomes before freezing temps set in. They can be stored over winter then replanted next year. Your cannas multiplied from the rhizome which is a large root that grows horizontal underground. It sends up new shoots as it spreads. You can save the seeds and start new plants with them, but they multiply so quickly from the rhizome that it is not necessary. You can start them indoors early and then re-plant them after the last frost. Again, someone who overwinters cannas would be able to tell you better than me how to store them. When you dig them up and wash them off it will be easy to see how these plants grow and you will have an idea of how to divide them. If you cut the rhizome into larger sections the plants will get off to a better start next year than if you were to cut it into small segments.

I live in Missouri next to Illinois, I have been growing cannas for the last 7 years. Through research I have a method for over wintering my canna rhizomes that has never failed me. I dig them up after the first frost has killed off the foliage, trim the stalk to about 2 inches, rinse off all dirt/mud from them, check for any damage or signs of disease,(cut away any yuck) and place them on a rack to dry with a fan on low to dry them. After about a day of drying, I then place them on top of dry potting soil in cardboard boxes (no lids, open to the air) and give a mist of Fungcide, and will typically keep a small fan blowing for circulation throughout storage in a cool dark corner of the basement. Every few days I check them and give them a mist of water. I am pretty medothical about making sure that any soft foliage dries so as to not promote fungal infection that will turn them to mush by spring. Last winter I tempted fate and did not dig them up, the winters had been mild for years. I mulched them and Well, last winter we had record snow fall and lots of moisture. I lost half of my collection, they were mush. Only the rhizomes closest to the foundation of my house made it. Happy to report that the ones that did make it grew and flowered beautifully :)

If the storage area is extremely dry, I would probably find a less arid location rather than spray the rhizomes. Most northern gardeners, I think, just clean them, let them dry, & pack them in straw, peat moss, etc, & store them in a cool, dark place that does not freeze. Best luck!