This mod started when I discovered that the well-known technique of reverse-pickpocket clothing onto an NPC would work in reverse, if the right conditions were met. The clothing had to be zero-weight, for example. It just needed a bit more work to be able to swap clothing items, to give the appearance of removing just a shirt, and leaving the rest.
The mod contains before/after pairs of clothing, and the script support for the process.
I tested this out on the proprietor of mALX's Wobbly Goblet Inn, which I was beta=testing, and sent it to her as a potential add-on to her mod (just like the poster). The last version of that can be downloaded here in case anyone else has a need for it.
Buttoned waistcoat
Not just shirts.
I don't recall if there is a dependency on the Wobbly Goblet / Lucky Mudcrab mod. I can't currently run Oblivion to check.