Here in Texas we cut them when they freeze or want to stop them from getting any larger. We do a simple cut at an angle then watch for rot if it should as rot will go to the root if allowed. Aside from this there isn't anything to cutting the stalk-trunk. I have cut them with a plain old kitchen knife. If I were you I wouldn't cut it unless you have to do so. We also have to trim leaves from time to time as they get ugly.

I'll try to make some suggestions as I am in the state. Most of us that dig them up or bring them in try to do cold dormancy. That is usually cold and dark, like a basement or under the house. In Master Gardener's training the tropicals section said to do cold and bright as the plants metabolism will be slowed down but can still use the light energy to fuel the slow processes that are going on. So if the plant fits into the sun room uncut, then you may just be lined up with a perfect situation. The million dollar question, does your unheated sunroom freeze? If so it's a no go. Good cold storage aims for 45-50 degrees, at which point the plants literally stops moving and just waits for warmth to wake up and grow. Any colder and damage will happen. Any warmer and it will continue to try growing. Depending on how warm that may work for you. I don't have great overwinter success but I do get them through. Those are the basic options.

And about cutting the stalk. As long as the plant is in decent shape a cut stalk always gives back another. Whether regrowing from the same trunk or dying down and coming back you should never lose a banana from cutting back, only time.