Does 70% alcohol sanitize enough to kill the wart (on hands) virus enough to no longer spread on a dry surface?

No. The wart virus is very tough to sanitize. Disinfectants like Lysol (60% alcohol) do not contain a high enough % alcohol to sanitize the HPV virus which causes warts. Exposure to 90% ethanol for at least 1 minute can disinfect the virus. The best way to prevent spread is to keep the wart covered with a bandage. I hope this helps!