Hello, and welcome to FDMB,
Long story short: You do whatever you can do.
However, you may find that 'what you can do' is a lot more than you initially think is possible; so I wouldn't draw the line at what you think you can and can't do too soon.
If you actually do literally faint at the sight of blood then testing your cat's blood glucose may not be for you. If you just mean that blood gives you the shivers then you may be able to overcome that.
There are quite a few folks here, me included, who were needle phobic; and who needed to go through some kind of process of desensitization.
(I had a fear of syringes and found it helpful to repeatedly practice drawing up water into the syringe, and then injecting into an orange. It was as though my hands got used to it first, and then my mind followed after...)
Are you coping with the insulin shots yourself? Or are you getting help with those?
Urine glucose testing can be helpful, but it also has it's limitations. It tells you how much glucose is in your kitty's urine since she last peed, but it doesn't tell you the 'highs and lows' of how the cat's blood glucose is throughout the day.
Testing should not hurt the cat at all. There are very few nerve endings in the outer edge of the ear. So I think it unlikely that your cat has disliked the tests because of pain. Some cats dislike being restrained, some cats don't like strangers (or certain people). And it's important to remember too that this is all new to your cat. S/he doesn't know what's going on and is probably feeling a bit jittery. Your own feelings will make a difference too because cats pick up on our moods. The more relaxed you are, the more relaxed s/he is likely to be.
I thought my cat would be impossible to test. But I found that I could crumble a few treats and test him while he's munching on those.
If you wish, I'll post a link to some example videos showing various people testing their own cats. But I won't do that unless you want me to, because the videos will show a tiny blood droplet on the cat's ear.
Best wishes,
Eliz