I had TC and gave the cold cap a go. My sister had just died from BC the year before, I'm now raising her kids and I wanted to spare them the visual reminder. I actually wasn't bothered about losing my hair.
I don't think the cap was fitted properly. It absolutely must have full contact with your scalp. Mine was firm at the edges, and I didn't lose much hair there. But above that band the contact was patchy and then absent. As a consequence a lost all the hair in the top of my head, and big patches below that. It looked dreadful and the mess was distressing and annoying. So after two goes I stopped.
If it ever happened again I wouldn't bother with the cold cap, but as I said, I didn't really care about losing my hair. I know it's tremendously important to some, but it wasn't to me.
If you do go ahead, make sure the cap is well fitted and keep pushing ir down.
All the best, and let us know what you decide. K xox