Wash your hands well, and you'll be fine. There is a difference between sterile and sanitized - sterilize means (roughly) to destroy all germs and microorganisms, typically by boiling or irradiating. Unless you're at the CDC working with bioterrorism materials, you're not going to need a truly sterile room or environment. Sanitize means to get the germs down to a low enough concentration that they won't contaminate your wine - the alcohol does a pretty good job of killing whatever bits you don't kill or weaken by washing/disinfecting your hands and equipment.
Looking at in reverse, if the room and equipment was actually sterile, the yeast fermenting your juice (and you!) would be dead too!