I think it would be easiest to paint by pouring it in batches into a large container that you can then add paint to and agitate - quite a bit of effort though, you need somewhere to put it while it dries, and you'd need whatever large container you can find with ability to fully agitate to fully cover in paint. Plus, rubber is flexible, paint less so, so I'd guess more chance of the paint coming off anyway.
Alternatively, they have shredded tyres around a playground at Legoland (only place I've seen it) and there is no issue that I could see with it being dirty or black marks coming off. I don't think tyre rubber is inherently dirty or black - I think tyres are dirty because they're always on the road picking up dirt and tyres dust from use. Personally, I wouldn't worry to paint and would stick with the shredded tyres as is.
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