I don't have anywhere near the talent for embellishment that many of the folks here possess.....but I do clean/sharpen knives for my friends and others.
There are many products that will get in the joint/pivot area and help "float away" the bad stuff. One that works for me, and most folks have around is WD40. Here is
my routine:
1. Using the small red tube to concentrate the spray, shoot a
little bit in the joint/pivot.
2. Work the action 10-12 times.
3. The same amount of WD40 once again.
4. Work the action again.
5. Let it sit on a towel/rag on the backspring area for 5 minutes.
6. Work the action again.
7. I went to a beauty supply store and got eye makeup applicators (yes, I look way cool!

) that are like a plastic toothpick with small foam sponges on the ends. I use these to then get in the pivot area and between the liners and springs. No fuzzies or strings left behind, like cotton, no scratches like what might happen with a pipecleaner.
8. Blow the knife out with compressed air.
9. Wipe it down with a soft cloth.
10. Oil the joints and treat the scales, if you're so inclined.
Might be anal....but it works for me.....
Bill
P.S.
Or, you could use hot water.