I saw your question a few days ago, and began to do some digging. My primary source for this was Franz Ferdinand's international travel diary, which is reproduced here online. The archduke traveled around the world in 1893 for the better part of the year. Heading east from Vienna, he departed on an Austro-Hungarian cruiser, the SMS Kaiserin Elizabeth (which was later scuttled in Qingdao Bay shortly prior to the city's capture during WWI.) He visited the near East, Sri Lanka, India, Singapore, the Dutch West Indies, Australia, German New Guinea, Canton, Hong Kong, Japan, then the United States and Canada. He was briefly present in Chicago for the World's Columbian Exposition, before heading for New York and then returning to Vienna, via Paris.

I searched for 'charm' "talisman' "token' "luck" "rabbit" etc, and their approximate German equivalents. No matches. Searching for "mysticism" and 'superstition' did not yield much either. As Franz Ferdinand was an avid (some say voracious) hunter, perhaps he wore a token or medal of St. Hubert, the patron saint of hunting? I branched out further looking for anything he might have bought /received as a gift. I found a few mentions, but nothing 'portable' or worthy of special mention in the luck context, most just specimens for museums entrusted to him, or larger art objects for his own personal collection. There are several entries detailing some of the hunting trophies he took - his first tiger, his first elephant. Perhaps they might have been formed into keepsakes or carrying pieces.

In addition, there is a current Austrian/German custom of wearing 'lucky charms" or "glucksbringer" near Christmas. I was unable to find a source detailing customs from the 1910's, but the modern application runs towards the stereotypical "lucky charms": rabbit's feet, four leaf clovers, horseshoes. This may be a tenuous connection as he was killed in the summer, not the winter. Best of luck with your further search - he was a much more complex person than most give him credit for. I found it ironic that in 1893 he, whose death was one of the sparks of WWI, visited Nagasaki, one of the final endpoints of WWII.