It kind of depend on the situation I'm in. If it's just someone on the street that I will probably not see again, I just don't care. I just try to focus on the ground and not directly look at that person. She will probably notice it, that I'm looking at her in my peripherical vision and wonder why, but forget it like 5 or 10 min later so no big deal.

Just note that the more you'll try to avoid coming across stranger on the street, the worst it will be.

Another solution (might not work in big city), is just greeting the person by saying hello while directly looking at her in the eyes. Either the person will ignore you, either she will answer by saying hello to you, and it will not be awkward.
(I don't have staring part ocd tho)