Danny, we don't have a bin system but clear bags for recyclable materials. Shredded paper is not accepted for recycling but must be put out as refuse because of the risk of metal and plastic contamination.
Yes they all have different rules - my council will allow a 'small' amount of shredded in the mixed recycling bin (paper, plastics, metals).
Very good point about animal bedding - most shredder contents will contain some degree of staples, plastics etc
I checked my local council recycling rules which are contradictive. Their leaflet states they will take magazines, glued or stapled but not shredded paper because of the staples. I have tried talking to them but have discovered another thing they don't take, phone calls.
Vulcan, although there i no problem with my council accepting shredded paper in the re-cycling bin they do advise stuffing it inside a cereal box etc to avoid it flying about.