I've never had any of my cats shaved, but I know a cat who is shaved every summer, and she feels so much better. This kitty is loved but not well cared for, she has a heavy thick black coat, and she mats something terrible. I work on the mats when I am there, but I don't see her often enough to make any real difference. I nagged these people for years to have her shaved in summer (when the matting is the worst) and they finally started doing it last year.
Here's a picture of her in winter, enjoying the self warming bed I made for her some years ago.
Anyway, if you think it will make Shadow more comfortable, I would say why not. Just keep her out of sunny windows until the fur grows back a little, to protect her from sun burn.
Also...for whatever groomer you choose, get recommendations from people who have been there, first. And stay with her during the session.