What embarrassment? Close the curtains around your bed change and open them again, hey presto. Personally I don't have the problem, I undress or change in front of medical staff with no worry.
Know that they've more than likely saw worse. Severed limb, someone getting stitches, tons and tons of blood. They don't care if they see you undress.
They should give you privacy.
Oh ok, is it coming up?
I've known a few hundred nurses and they all say the same thing.
They're completely un-phased by male anatomy.
Just think about how embarrassed they feel as well.