There is nothing wrong with a man greeting a non-Mahram woman with Salam, without shaking her hand, if she is elderly. However, he should not greet a young woman with Salam when there is no guarantee that there will be no Fitnah (temptation).

Some tips on how to lower your gaze: 1- bear in mind the fact that Allah is watching you, 2-seek the help of Allah, 3- avoid places where a person feels he will be exposed to the temptation of looking, 4- do a lot of nafl acts of worship, 5- remember that the earth on which sin is committed will bear witness.