Well, it might be possible. If you truly have eczema, it's not an incurable disease, it's just a fancy name for itchy skin from dryness or whatever. If you can fix the cause, if you can find it, that fixes the problem. For example, for some people it's not eating a diet sufficiently rich in essential fatty acids. For some it's a side effect of antibiotics. I don't see how hair makes something more moist -- that doesn't really make sense -- and shaving will have to be repeated regularly, make the hair stiffer once you start shaving it making shaving even more irritating, and irritate the skin. If moisture is the problem, it's more likely a recurrent fungal infection. I have no idea what you have or the best way to rid yourself of it, but it's hard to see how shaving the area does anything but irritate it more.