I'd be too worried about anything wood myself.
I know this does not satisfy the criteria of the OP, but...
For me, if the playability and tone of the Outdoor Ukulele was good enough, I'd likely go with that and replace the tuners with either sealed-geared tuners, or Gotoh UPT tuners, with are also sealed with the hope that the sea salt cannot get inside and corrode the gears. Barring that, with the existing tuners, I'd put a copious amount of lubrication on them before exposing them, something like bearing grease or even vaseline, and regularly check or re-apply as needed.
However, replacement tuners, similar to the originals on the OU, with the SAME mounting hole positions, are available on Amazon for about $5 or on CB Gitty for about $10 per set of four, so if they need to be replaced, it's not a big cost, and takes maybe no more than 20 minutes total if you have to remove and replace the strings with a manual string winder, and the only tool needed is a phillips head screwdriver.
Either an HPL uke as mentioned would be my second choice with similar considerations for the tuners.
My Fluke and Flea ukes are my favorites and I would consider taking them to a sea-salt environment a level of abuse that I would not subject them to.
Standard friction tuners are not an option for me, under ANY circumstances. I hate them with a passion, and the frustration they cause. Easier to use and modern replacements are everywhere, so if one were to suggest friction tuners, please understand that they are not now, nor will be anything I will want to use. That's just me.
Please understand that I am not judging nor condescending folks that love friction tuners, but
I prefer literally ANYTHING else.