Snychronize particle start frame to keyframe


I hope I’m asking the right question. I created a welding stick and emitter object that throws sparks when the stick touches metal. The problem is that some of my motion of the stick is too fast so I want to slow it down, but when I try scaling it in dope sheet, my particle start frames don’t scale with the keyframes so I have to go back and manually reset them all.
Is there an easier way…I’ve got nearly a hundred to fix.