I would say the Spinach, Lettuce, and Cilantro would be the safest things to plant there.

Lettuce loves afternoon reprieve, most cold season crops will do exceptionally well if you mulch the soils heavily (to keep soil temps down - bolting has to do with soil temps, not air temps) and plant them in your shaded area.

I kept broccoli producing all summer from a bunch of plants with a 4 inch layer of mulch (loose hay scattered around them) Instant read thermometer measured 60F @ 4" deep with the mulch (constantly), and just about equivalent to air temps without mulch.

Your lettuce, spinach, cilantro, any other herbs, should grow there.

Edamame, tomatoes, your squash and all that loves the full son, so, I'd do it that way. Glad to help!

Here is a link that might be useful: Mulching cold season crops for summer production

Has anyone tried squash in partial shade? I know they are sun lovers but I really don't have any full sun spots available since they get sooooo big. I may have to forego zucchini this year. :(

6-8 hours of full sun is ok for most any vegetable. Shade your cool season crops with peppers and other taller ones.
I am in Texas 7/8, so I can grow almost anything in just 1/2 day sun. In fact they actually do better without our blazing afternoon sun. Good luck!

Any leafy greens would be good.. Now with the squash, cukes and other vines, they might work as well.. Here's why, because they are not stationary in that one shade spot you stuck them in, you could train them up the fence to the light, be creative.. A have a similar problem to your fence, my blueberries get shaded most of the day, however once they reach 3-4 foot they are getting all day sun!! If that was a fence in my yard, I would use chainlink, chicken wire, anything that does not block the light out.. If you didnt invest to much money in the fence, maybe you want to go with a transparent fence? Your husband probably gonna kill me - "you're telling me I have to build another one!", to funny...

Good luck,
Joe

I have a 6 foot wood fence around my yard. I usually use the fence as a trellis. I've had good luck with cucumbers and winter squash growing up the fence. One year the cucumbers reached the top of the fence and grew into the neighbors bushes reaching about 9 feet high.

Do you use lattice or something on the wood fence to create a trellis?

You could use a cattle panel on the fence. In my case it still helps to secure the vine (I use tomato clips, but tomato ties of any sort will work). Zucchini do make it in part shade, but long term, you will have to diversify into more greens. The spinach will be done in May, the lettuce in June. At that point you can only plant fall greens.

I use rolled fencing, maybe it's 1.5 inches by 3 Inches rectangles, and a staple gun.

Awesome, thank you for all the suggestions!