I know that golfing on Shabbas is not a Shabbas activity, but is there anyway to permit it? How can a frum Jew play in PGA events that are Thursday, Friday, Saturday and Sunday? If we play in an eruv, avoid carrying (if still necessary), avoid hitting the grass, is there a permissible way to play and still be a kiddish HaShem?
The appropriate behavior to generate a Kiddush Hashem would be to avoid playing on Shabbos. Take for example the behavior of Naama Shafir and Doron Sheffer. Both are excellent basketball players whose adherence to the spirit and laws of Shabbos proclaimed the unique nature of Shabbos and those who stubbornly follow Hashem’s will.
If you are believe that golfing is not an appropriate Shabbos activity, then you should uphold the sanctity of Shabbos. Such challenges are the kind of things why Hashem puts us here. We need to show Him we care. By accepting to fulfill Shabbos the way you know it should be kept, your “Shabbos experience” in the next world will be more pleasurable than any golfing ever done at any time.