I too highly recommend a wrap/carrier/sling, something to help you carry the baby but have your hands free. For showers, the bouncy seat right outside the shower with me singing and peeking at DD was only way to get through without much crying. My DD hated laying down flat, but would tolerate being upright in the bouncy seat for a bit especially if she could see me. I also used it so I could use the bathroom without having to hold her. It doesn't work for everyone, but a cheap bouncy seat was a lifesaver for me and my wrap, sling and carrier were also a great help, even though DD didn't like being in them except when facing out so I couldn't use them much until she was older.
And yes, swaddling can help sometimes too, a baby that is fed, had a clean diaper, etc. and you need to take a shower or whatever, if swaddling helps calm them, that's great! I do think swaddling gets overused by some, but I agree it is like pacifiers or any other parenting tool, it has to be used with care and attention and not overused when the baby does have a legitimate need to be held and comforted. However, on the other side of that, those tools are great to use for limited periods of time when the baby's caregiver does need to attend to something, that is what those tools are designed for!