We've been thinking about this! we currently have a very nicely made wooden storage shed with our yard tools in it, but we've been contemplating using that for the chickens and just attaching a run to the back of it and
making a corn of it their's. I guess I just don't know... they're probs gonna poo on all our tools and stuff huh?
You did not say how big that shed is or how much room you'd give them. How air-tight or well-ventilated is it now? How cool does it stay in summer? Does it stay perfectly dry when it rains? What kind of floor does it have, dirt or raised wood?
When you say yard tools I envision a wheelbarrow, rakes, shovels, and such. Dust from the chickens would not hurt those. But lawn mowers, edgers, power tools, and other things with motors may be more of an issue.
Chickens create dust. Part of that is dander, bits of skin and feathers. They shred bedding with their scratching. If they are on dry dirt their scratching can turn some into dust. When their poop dries their scratching can turn some of that into dust. Many people do not appreciate how much dust they can raise. It can be a lot more than just dander.
I made my coop by converting a 12' x 60' loafing shed into a storage shed. It stayed dry but had great ventilation up high and down low. It was metal. I made an 8' x12' end into my coop with adequate predator protection, leaving one wall metal, and using wood panels on the end and other side. Inside, I had a wall partly wood panel (T-111) and partly hardware cloth so there was great ventilation between the inside of the shed and the coop. I stored my "farming implements" (hoes, rakes, shovels, axe, etc.) in there along with a trailer, spare wood and wire. And of course the chicken stuff. The only motor was on my riding lawn mower and I covered that with a piece of plastic to keep the dust off.
Yes, there was dust but it wasn't a problem. If I'd had power tools like hand saws or drills it would not be good. Dust would be bad for them.
If the chickens have access they will poop on whatever is in there. If you have a wire wall between the coop and the rest of that shed they will generate dust, even just four chickens. If you build a solid wall around that corner you should be able to keep the dust out.
To me, that tool shed has real possibilities if it is big enough. How you set it up will depend on what tools you are storing in there.