I would trust him to do this, though I don't think I'd trust him to pick out regular underwear and bras for me. He's even agreed with me on this. We both know he'd go for the sexiest thing possible, rather than a functional piece of clothing. I think he'd be able to get the right size, too.
Hell yes! He shops for me better than I can. I can spend hours shopping and end up with a pair of socks and just frustrated that nothing fit me. I get sensory overload and can not focus on finding what would look good on me; however, my husband can walk into a store and see something in a glimpse and it looks fantastic on me. I do not seriously shop without him! He knows my body better than I do! That works out in many ways for me.