Hopefully, each of your bassoon swabs looks like this, with a tail on the end in case, heaven forbid, the swab gets stuck. A few years ago I experienced the unspeakable horror of getting a swab stuck....REALLY stuck, inside the wing joint of my bassoon. It took Chris Weait's swab extractor, the physical strength of 2 adults, and long distance coaching by repairman Carl Sawicki via speaker phone to extract that swab. It was not done without superficial damage to the interior wall of my wing joint, unfortunately. The bassoon still played after that, but I strongly advise all bassoonists to avoid the trauma of emergency swab extraction at all costs. I learned my lesson. I will never again insert a tail-less swab into my bassoon, nor will I insert a swab which is not 100% free of knots.
It's fortunate that I learned my lesson, because yesterday I experienced another swab incident. This time it was a bocal swab, which I have found to be the safest and most effective tool for weekly bocal cleaning. The swab simply broke, as you can see in the photo below, as I was pulling it through the bocal!
Thank heavens it had a tail, and I just pulled the swab back out by pulling the tail. If there had been no tail on that swab (many swabs lack tails!) I suspect that my bocal would have been ruined.
This reminds me of quip from the late legendary bassoonist Norman Herzberg. Whenever a panicked student with a swab situation contacted him for advice, he replied that the best response to a stuck swab was "dinner and a movie" followed, of course, by renewed effort with a fresh perspective! (Back in those days, I don't think swabs had tails....)