I’m carrying Hodge silk swabs, designed to pull all the way through an oboe or English horn. They are made from 100% silk and come in a variety of colors. They have long tails for safety – if they get stuck you can just pull them out backward!
I also have thicker, absorbent microfiber swabs which are NOT designed to pull all the way through – but which clean all joints more thoroughly than silk.
I use both, for DURING playing and AFTER playing, respectively.