You could ask your pediatrician if they do the test. They'd probably be okay with you holding or nursing the babe while they do it. And tell them to warm up the heel -- it makes it a lot easier.
I had to do some serious bullying of the nursery nurse in the hospital about this test. She first insisted that the test had to be done in the nursery because "all our equipment is there." I raised my eyebrows and said, "I believe the 'equipment' for a PKU test is a needle and a card. Are you honestly telling me that those two items are not portable?" She stormed out, came back with the needle and card, then insisted that the baby had to be in her bassinet, unswaddled, and flat on her back in order to do the heel prick. I asked nicely for an explanation of the medical necessity for this, and she said, exasperated, "because you have to put her down sometime!" So I just fixed her with a steady glare and said, "I'm sure that's true. However, 'sometime' does not have to be the first time anyone sticks my newborn with a needle. If there is no medical reason to do otherwise, I'm going to ask you to attempt to prick her heel while I'm holding her." She huffed in frustration and said, "I'll try." (She's lucky I didn't throw her out and say, "go find someone competent enough to do it without 'trying.'")
All of this is to say, just because they do hold the poor child down on a table in a separate room to get the heel prick, doesn't mean there's any particularly good reason to do so. Fight them on it, if you have to, until they give in. You have the information, and the right!