Out of sheer ignorance: what are the implications of not having the proper paperwork? Do Japan's street policemen take note of suspicious looking bikes and follow up with their owners?
The police stop bicycles and ask who it's registered to. They can look up the registered owner from the registration sticker. If you stole the bike then you don't know the name of who it's registered to. In general there's no requirement to carry ID (apart from for foreign nationals) so police can't rely on cross checking against the ID people are carrying. Also, bicycles might be registered to a friend or a family member, so knowing the registered name and providing an explanation should be enough.
If you have no idea about who the bicycle is registered to then the police will likely make further investigations.
I have been stopped when driving suspiciously at night. I do not know what exactly constitutes suspicious, but the main thing they do is check whether your bike paperwork is in order, and (as a foreigner) that your residence card is valid.
If you have no idea about who the bicycle is registered to then the police will likely make further investigations.