If I'm not mistaken many people will use fungicide when they are growing seedlings to prevent "Damping-off". This is a fungal infection that attacks seedlings before they emerge from the soil or just after they emerge.
I've never used a fungicide with cuttings...
To avoid fungal infections with cuttings I think it's more about using a sterile soil than applying fungicide.
Read this article from Brent Walston, it may be helpful.
http://www.evergreengardenworks.com/cuttings.htm
The leaves are drooping because the amount of moisture being supplied has been greatly reduced. You'll probably lose some leaves before things get better. Just be patient and don't drown the cutting. Good luck.