I personally think this is a fantastic idea, and that there is very little if any to no risk of it damaging your wood!It's sold at fungi.com and is meant to be diluted in to regular veggie chainsaw oil.
Spores need a lot of moisture to germinate. Whatever they grow on needs to be very moist as well. So assuming your not leaving your logs out in the rain for long periods of time and whatever you are using the wood for it is dry mushrooms or fungus will never grow. But that stump that's still in the ground outside in the elements, it will have a higher chance of growing mushrooms on it and decaying more quickly than if it didn't, if you use spored chainsaw oil.
It can also be used as a sort of preventative measure against the forest blight causing parasitic 'honey mushroom' AKA the Armillaria species of mushrooms that have thick black shoe string like mycelium that takes down tree after tree and spreads quickly.
It may be more expensive, but you can ALWAYS make your own spore prints from wood loving mushrooms that you have either found or purchased from the store or market! There are instructions or rather ratios for making it yourself in Paul Stamets' book Mycelium Running. I don't have the book with me but will post when I find it. One may be able to find it online somewhere.