I use Neem Oil too for fungus control on fig trees. It's organic and "safe". But I've never tried using it on new cuttings. Interesting idea. I guess I never tried this approach (knocking out mold/fungus on new cuttings this way) because I read on here about using bleach and water (1 part to 10 parts) to wash cuttings, and then making sure to use a gritty mix that drains well for rooting (and careful to avoid overwatering). I guess the bleach isn't organic, but I didn't have a problem using it in that concentration. Also I've used bleach in that concentration for years to clean used pots that I buy. It kills lots of other pests (like root knot nematodes). I rinse them well with water after using the 1:10 mixture, and dry them before I use them.
I guess preventively knocking out fungus/mold in cuttings other ways seems interesting though. I'm interested to hear how this thread and your experience turns out.
Mike central NY state, zone 5