Would this recipe work with Tahini or Cashew Butter? I wonder if I should change the sugar quantity in any of these cases.

Tahini has bitter notes, so the cookie will have a completely different character - and may need more sugar to be palatable to most people. Tinkering with sugar can alter the structure of the cookie (generally, it tends to make a cookie too brittle). For that reason, I'd substitute the cashew butter. If I wanted to make a tahini cookie, I'd look for a cookie recipe that was developed and well tested with tahini. ;o)

She says in the head note that it would work with tahini or cashew butter. A cup of sugar for a cup of nut butter seems like a lot to me. You could combine the nut butter with the sugar a little at a time, tasting it till it’s sweet enough for you, before you blend in the egg. Sugar helps with browning, so if you cut it back too much, the cookies will be lighter in color when baked. Also, if the nut butter you use is not salted, I would add salt. I use Diamond Crystal kosher salt— 1 teaspoon for each cup of sugar. If you use another brand, or table salt, you’ll need about half of that.