I do not think this works. nut weed inhibits other plant growth. Cyperus rotundus gives off "chemicals" that slow grow of neighboring plants. Parts are edible and was used in ancient times to prevent tooth decay. Can you show a study where this is true? Cinnamon is a good substitute for root hormone products - rub a little ground cinnamon on the cut
I would definitely mix in some compost with your garden soil as this will improve the structure of it. The dusting with fungicide is useful as it prevents the risk of infection, however, if you keep an eye on them and be ready to spring into action then it could be worth trying without . As for planting, I would personally keep them inside for a while, give them a chance to strengthen up before putting them outside in the elements!
Cover the cutting loosely, pot and all, with a plastic bag or plastic wrap and keep the soil moist. Putting a tall stake into the pot will hold the plastic away from the leaves. If the plastic touches the leaves, they remain wet and can succumb to a fungus disease. Along the same lines, make sure the condensation can escape from the plastic or the stem will rot.