What are safe alternatives of electrical tape?
As far as safe, duct tape is conductive in some brands especially when wet. Scotch tape is not conductive but it lacks the dielectric properties especially over a shattered globe to be considered safe. To be safe don't use this string of lamps. 

Festoon lighting is normally used outdoors or on construction jobs. With a damaged lamp that gets wet a greater shock hazard is there. It would be better to remove the bulb than to have the broken parts extending from the socket.