Klar, if your drinking is not affecting your family, why would not drinking be a big impact item for them? I would be a little cautious about tattooing a big red A on your forehead. Alcoholism as a label carries a lot of baggage and misunderstanding. When you tell us you are an alcoholic, we know what you mean. When you tell someone else, it may mean something entirely different. In many respects non-addicts have no idea what it is like to be addicted, anymore than I know what it is like to be blind. Empathy has limits.
I am about six weeks sober. Like Murray, I have talked with my wife about not drinking. Some time in the next month or so I will talk with my sons about it. If a close friend or other family brought it up, I would likely talk about it to a certain extent. For me, it is like talking about religion, there are very few people I would discuss either topic in depth with because the conversation is intricate and takes some effort from both parties, it is very personal and requires trust, and frankly very few people actually care what I think.
Whomever you talk to, make sure you are doing for the right reasons. I have known many people who wear the addiction label a little too proudly. It gives them an excuse to screw up later and put the blame on the disease.