Find a local painter or cabinet shop that finishes their cabinets and ask if they have steel paint buckets to give away. The recycle companies don't like them, they bounce around in the shreader and have paint residue. Most is lacquer, turns to dust or a fragile cake icing like stuff once exposed to air long enough. The binder in the stuff tends to crackle if it dries too thick, AKA crackle paint. In a few weeks you can bang the side of the bucket and the dried paint falls off and is safe to dispose of in the garbage once dry.
Use a plastic bag if you are worried about residue in the feed. Most buckets have tabs that can be bent down with a hammer or with your hand to secure the lid from most critters.
I have to give the buckets away on Craigs list once or twice a year to get rid of them. People use them for feed buckets, excavating soil under houses, or as fish structures in ponds.