" I have heard that wearing a wedding ring alerts women to the fact
that I'm married and not looking for outside interactions, while not
wearing a wedding ring tells women I am available."
Actually, some people think the opposite! A former work colleague who had been married less than a year once pointed to their wedding ring and boasted to me that the ring actually attracted more advances from women (I decided to spare you the expression he used because it was quite offensive). But I do believe there is probably some truth in this - some people (because I'm sure that this could apply either way and to either gender) may actually see chatting up a married person as a challenge. I have also heard it said that some single people seeking stability in their own lives actually pursue married people because they imagine that person is more likely to be committed. In cases like this a wedding ring could actually be a visible sign that you've got what they are looking for! Of course, this seems faulty reasoning to me - anybody willing to leave their partner for someone else is the exact opposite of "committed"!
Without moralising or getting into psychology, I think it is fair to say that people who seek extramarital affairs, and those who carefully safeguard against affairs think quite differently from one another. So chances are they view the wearing of a ring (or not wearing one) differently too.
To answer your question, the best way to avoid unwanted advances is by your words and actions. Whether or not you wear a ring in my opinion will make no difference. If someone is looking to have an affair then a ring will not put them off.
If someone does make a suggestion you do not like, say:
"I'm not interested."
There is no misinterpreting this. Some people believe that saying "I'm married!" can be interpreted as an excuse and not a rebuff.
If you feel you would like a visible, outward sign that you are happily married other than wearing a ring, why not keep a photo of your wife/family on your desk, or wherever you are facing these challenges?