They'll take them back. I worked at Target a few years ago, and their return policy is surprisingly lenient. Just tell them that the shirts are defective - shrunk too much when washed. Target will donate them to Goodwill. If you don't have your receipt, and you paid by credit card, they can look it up just by scanning that credit card, even if it's not theirs. I love Target, can you tell?
Oh and BTW my hubby has the same trouble with shirt sleeves. If you ever figure out a good place to shop, let me know; he hasn't had a long sleeve shirt that fit him for a very long time.