Oh, Andrea - my veins are shriveling in sympathy with you - glad I don't need any blood drawn today. They run (dive?) at the mere thought of a needle.
Have you tried soaking your arms in hot water when it's time for a draw? It helps to bring my veins up and frankly, in my nsh opinion, the techs can just wait for you - might as well kill time waiting for you to warm your arms as dig around.
I found that if I was icky enough they only sent their best techs (they even sent up an oncology phlebotomist) with the smallest needles.
Then they sent me home early with instructions to get my blood drawn at the lab in two days.
We'll be waiting for news of your surgery.
Geesh - you're not going to make this an annual event, are you?
Best of luck, kick the techs, and my prayers are with you this week.