Will my cat be okay without a head cone after being spayed?

My cat was just spayed, and the vet didn’t give me a cone at first because she wasn’t trying to pull at her stitches. But I asked for one anyway since she’s my first cat and I wanted to be safe. Now that I’ve put the cone on her today, I’ve noticed she’s having trouble moving around. My house is old with narrow halls and doorways, and she keeps getting stuck.

I want to know if she will be okay without the cone. What might happen if she does mess with the wound? The vet seemed fine with not using a cone, but all the cats I know that have been spayed by friends and family had collars. I searched on Google but couldn’t find a clear answer, and I’m worried about her.