I'd not quarrel with your doctor....but there are conditions and extremes presumed here that are seldom in place or practice. There are times when the '..bloom..' from the spawn are particularly concentrated and dense. This condition is seldom encountered close inshore at beaches and figured on a parts-per-million basis, quite probably no worse than any other of the microorganisms that inhabit the ocean. As for specific wounds, more often than not, other factors---microorganisms that may have entered from contact with the original source of the injury (always a source of concern, other foreign matter (always concrns), improper care and cleaning of the wound at when it occured originally, etc. Any of these factors are as likely to cause leter problems as '..reef spawn..'.
There is also the practical aspects of the concern. The local newspaper publish the daily tide tables, phase of the moon wind direction, expected air and ocean water temperatures...but I've yet to see a '..Reef Spawn Index....or state of the tide and local current information which would indicate potential '..danger..'.
Over the years, I've been perhaps more concerned than many with the state of the Tides (and by extention the phase of the moon) ....usually printing out the local Tide Tables abd carrying them with me (for snorkeling purposes and the surf and beach conditions most likely at '..our beach..' When your wife is a semi-famous sand sculptor...and you're the poor lackey who has to pile it on the rocks for her, you learn to pay attention to not-so-petty-little-details') and I'm sure that on any number of occasions over all of the days at the beach, over all of the years that we must have nicked, scraped and cut ourselves and gone into the ocean durin 'spawn' periods....and we've still got all of our fingers and toes.
But if 'reef spawn' is that much of a concern, bear in mind that it usually occurs during periods of Full moon...so avoid the ocean during these few days of your visit.