How many chickens do you have and how big is that converted dog house? Many of the recommendations on this forum suggest having 4 square feet per chicken in the coop. That would mean about 3 chickens max for most of the dog houses I have seen.
I am currently using free paper shreds which I make at home with my 12 sheet shredder. Paper shreds are very light. Every couple of weeks, I throw in another bag of paper shreds into the coop. The chicken poo and shreds stay in my coop all winter and does not get cleaned out until spring. The chickens will scratch and peck the paper shreds for the chicken scratch I throw into the coop. That scratching causes the poo to go down to the bottom and the fresher paper shreds works themselves to the top.
My coop does not smell using that system of deep bedding. But I also have a very high ceiling in the coop (about 8 feet) and built it to have almost 8 square feet per chicken. Lots of factors will affect the smell in your coop and how often you would have to clean it out. If you use deep bedding, or deep litter, then you should not have to clean it out but maybe once or twice a year.
My concern is that the dog houses I have seen are pretty small and have a very low roof. And none of the dog houses I had in the past were meant for chickens and cleaning out of the dog house. I mean, I had to literally lift the roof off our dog houses to get inside. Not easy for cleaning out if you have chickens.
If possible, I would suggest again trying a deep bedding solution starting off with maybe 3-4 inches of litter, and fluffing up the bedding or throwing on fresh litter as needed. I usually start my chicken coop with about 3 inches of litter in the fall, and by spring time, I have about 12 inches deep of litter. But I live in the frozen north and our chicken poo freezes solid and does not smell. Nobody around here, that I know of, cleans out their coops until the spring thaw. The deep bedding, or deep litter, does a great job for us in keeping everything clean and smelling good throughout the winter.
I hope you recover well. And while you are healing, take some time to rethink your backyard flock setup and maybe find a better way that works for you. I mean, I only clean out my coop twice a year and I don't have any health concerns. If you are cleaning out the coop every few days, then I think you might be able to find alternative methods that would significantly reduce your labor. Hope all goes well with your surgery, and you are up and on your feet in no time. Take care and best wishes.