How much do you want to spend? I'd go out to my barn, find an old extension cord whose plug I had to replace previously, unscrew the plug, push the cord thru the hardware cloth, then reattach the plug. Because its easy, and I have repaired extension cords around. Faster than cutting a 1 1/2" hole in the hardware cloth, then rigging a way to reseal it. Also, my coop and run are ugly. So adding a sight sore is no big deal. I **WOULD** put a loop in the cord and zip tie it to the fence to reduce cord stress, of course.
Now, if my coop looks like the one my brother built (he does high end cabinetry commercially, and restores wood antiques as a hobby, I'd carefully cut a hole in the coop, mount a deep box exterior electric outlet with weatherproof in use cover, and install an inlet that allows you to plug the female end of the electric cord into it. and wire the coop internally from there - much as when you see a cabin wired for a generator hook up. Its considerably greater expense, and permanent.
If I was to split the difference? One of these:
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https://www.homedepot.com/p/AC-WORK...-Extension-Cord-with-Cover-IN515520/314101122