For tools I think it would be better to stick with the usual agents- bleach, alcohol, and lysol. I don’t think Chlorine Dioxide is going to work any better.
Using it as an anti-bacteria agent probably isn’t going to work well. Chlorine Dioxide is a gas. Usually it’s sold as a solution in water but as soon the solution dries on the tree the Chlorine Dioxide is going to be lost to the atmosphere. So the material will have no persistence. Most anti-bacterial agents and fungicides have a fair amount of persistence. They still work for days or weeks after application depending on which one it is and the environmental conditions.
Plus your going to have to spray it and I don’t think you want to breath a Chlorine Dioxide mist any more than you want to breath bleach. Technically it’s illegal to spray it since it was never tested on fruit trees and there is no label that tells you how to safety use it and what concentration you should use (at least in the United States… Germany maybe different).
You can spray Daconil for peach leaf curl and it works. For canker you can spray copper and cut the cankers out. Peach gummosis is harder if it’s fungal but I don’t think Chlorine Dioxide is going to be helpful.
You might take a look at this thread on using bleach as fungicide and people discuss issues that will carry over to the use of Chlorine Dioxide.