I agree, finding out their mail address through some third party is a bit like spam but there's nothing unethical in asking. So long as you come across as 100% honest, the worst that would happen is them saying, "I'd rather not."
I'd say put your address at the bottom as well, eg

Sincere regards,

Lisa Gergets

189 Makebelieve Drive
Townsville
YourState

That way you're making the first offering, and they'll probably find your too far away to be a stalker.