I do not know about the dog launcher but would stay away from it.
Even if legal, having a starting gun would be a very bad idea for an unsanctioned race. I had adjunct duty at a track meet one time and was actually handed one by the principle and unless I actually had it in my hand you really could not tell it was not real.
The hammer-shot I think would be somewhat of a grey area. To me it would boil down to if you fell into some kind of exemption like having permission to use it for a lawful purpose within the scope of your employment. For example, I teach high school shop and have two of them in my tool room and use them from time to time. I do keep the blanks locked up though.
Honor is a way of life, live it with pride
"Patriotism is supporting your country all the time, and your government when it deserves it."
- Mark Twain
Si vis pacem, para bellum