The phrase "few nicks" means there are only a small number of minor cuts or marks on something, usually referring to an object's surface. Full definition
Baby oil works just as well for shaving your legs as shaving cream, but it offers the added benefit of additional moisture (not to mention fewer nicks, cuts, and burns). (thefashionablehousewife.com)
That means fewer nicks and less irritation. (geekwrapped.com)
You shouldn't let this discourage you though, as we're only talking about a few nicks (compared to the gaping wounds you could experience with a straight razor) and it only takes a few shaves to get a handle on the proper technique. (primandprep.com)