Absolutely! I'm surprised I didn't think of that sooner, I bet it'll work like a charm.
Funnily enough, injections and blood draws are one of those things I don't flinch at! I have a rare blood type so I'm even a frequent blood donor, and I never jump at needles. I guess it's just sudden noises and movements that get me, but if I can't see it coming, I bet she'll have enough time to get it.