Tomb Sweeping Day is a happy or a sad holiday? Can I wish happy holiday for this days?

Basically it is a sad day. We don't usually say "happy holiday" for this day.

I feel that the holiday over here in China is for the respect of family. I am a Polish/American
that lives in Shanghai with his beautiful wife. When I go to the tomb of her father, I will say a rosary as a Catholic and burn incense and observe the traditions of the holiday.

What would someone say to another on this day? Is there a traditional greeting or parting that accompanies this day? A "happy holiday" greeting would be inappropriate, but what might be said instead?

A nice question. Chinese people don't celebrate Qingming festival as other Chinese festivals. So they don't say greeting words to each other during the festival. They just go to worship their ancestors and sweep their ancestors' tombs.