I don't want my answer to offend or insult anyone but I'll give you an old guys answer.
This was a problem in NY in the 80's.
Statute law decided the answer to cite or impound for us. And gave them latitude to come into compliance.
It has never been as clear or concise as automobiles.
Vessels were much like firearms pre Federal 1968 Gun control act. No standardization of the creation or affixing of HIN numbers. Each manufacturer did or did not crate and affix as they chose. Little inexpensive flat boats, although highly stolen were rarely numbered.
The legislature mandated that all vessels whenever under mechanical propulsion MUST be registered and MUST bear a HIN number to be registered. Data search as best as possible to determine whether or not their is an actrive file obviously based upon descriptions and photographs.
Then, I would contact the manufacturer, when and if it could be determined to see if they had a location for a confidential HIN on the vessels. Sometimes the NATB could be of use as well for their file of information.
When no number had been created by the manufacturer one had to be created and affixed.
The legislature by statute made both our DMV and Parks Depts. responsible for creating and affixing HIN tags with unique HIN numbers the Depts. created. Much like a salvaged motor cycle, automobile or snow machine.
Thus creating paper trails and affirmations and opportunities for false filings, false swearing and fraud and mail fraud for prosecution when possible.
HIN plates from vessels of that period can be quite deteriorated now 40-50 years later. Some manufacturers have provisions for re-issuing the HIN plates and capacity plates.
If you can find a grizzled old coastie or game warden they can sometimes be of assistance with these as well.
Vessel horse power was measured differently back then powerhead instead of lower unit as it is now. The old capacity plates tend to overstate the power a vessel can safely handle. Also the carrying capacity was based on an ADULT weighing 150 lb. not the average 250 lbs of today.
Hope that helps you at least a little bit.