Connecting string of cafe lights to power source sans outlet
Since that light fixture appears to be wired with temporary use extension cord anyway, why go through the trouble of wiring up a new weathertite box with GFI receptacle and approved weatherproof "in-use" cover (method probably required for code compliant install)?

Keep it simple. The items that I am suggesting are probably listed for indoor use only. I have a similar setup (in a similarly protected location) and have had no problems for years: socket adapter + lamp extension cord.