Is there a safe way to splice multiple lamp fixtures on the same cord?
You might want to look into using something like this...



Designed for paper lanterns.

Notice that the weight of the lights are supported by the cable and the socket, not the junction itself.  The problem with the product you linked to, is the weight of the lights are supported by the junction (given that it's not mounted properly). Over time the weight (or accidental yanking) could cause the junction to separate, leading to a potential shock/fire hazard.