Are these fine hairs from trimming the container from Styrofoam PS sheet?
My guess is, the formed parts may not have cooled enough to trim. Try trimming a cold part and see if the edge is still stringing out. The cutting edges of the steel rule knife trimming die can absorb heat when cutting with short cycle times. The knife edge should never touch the stainless bed. Some form of stop limits should leave .025-.05mm gap so the knives do not hit against metal. Spraying the knives with silicon dry lubricant periodically can help to avoid the PS sticking to the knife edges. If the PS and knife were cold when cutting, I cannot imagine it sticking or producing fine hairs on the edges.
Have you tried using a fan to cool the formed parts and the trim knives as they come off the forming die before they are trimmed?
If you have cooling water on this former, the stainless steel bed could be water chilled which would chill the edges of the PS as it cuts. Sometimes more space/time between the forming section and trimming section gives the parts time to cool.