What should I do with the grounding wire when connecting an ungrounded light fixture?

I have an extension cord with a grounding wire in it. I have cut off the female end and want to wire it to a light socket that will have an LED fixture screwed into it. This is for a garage workshop LED light. If the light socket doesn't have a grounding screw, what do I do with the grounding wire from the extension cord? I was going to put a wire nut on it, however I don't think it will fit inside the light socket enclosure.

Any alternatives?