I use my yyf multi tool because the really thin part is a little longer on mine. But that is if I don’t just unscrew it…
I love using safety pins!
Usually just a bent up paperclip. If it is a loose knot and I can grab it with my fingers, then sometimes with them.
My brother threw away all my toothpicks before I got to try them, so I had to resort to using a skewer/shishkebab thing (however you spell it). It worked well. I’ve found that the plastic flosspicks that I used were too short and flimsy to make the job easy, and paperclip was too wide and tore up the string trying to get it into the knot. But in the paperclip’s case I was trying to get out a years old knot that had been played anyway on a fixed axle yoyo.
I just use a needle with the tip cut off. you can stick it in the foam of your case. Works great! My brother just goes to my case when he gets a knot. 
Toothpicks. They can’t scratch the metal, they’re cheap, and they’re small.
I usually just take the yoyo apart. For old-school non-opening yoyos I use a tool that I have in my tacklebox. It’s like a long thin pocket screwdriver with a pocket clip, but with a tiny hook on the end instead of a screwdriver blade. Tackle shops sell them for undoing snarls in baitcasting reels.
I find using a tool of any kind can fray the string. May times I just replace the string. It is faster, easier and the string is more dependable and I can get back to playing much faster.