edit
No.
To expand a little on what Blackhawk said, no there isn’t any such place of which we’re aware. There’s a host of reasons, but the biggest is market size. While perhaps a few million of the cheapies are sold every year, the vast majority are sold as souvenirs (Cooperman), toys or just on whim. The cheapies in this market are VERY cheap as a rule, so there’s no real need for a resale market - if anyone wants one it’s just as cheap to buy a new one retail. My very serious opinion is that even most of the cheapies sold on eBay, often or at least occasionally at above-retail prices, are also impulse purchases.
As for mid-range or expensive models, I have no idea what most makers ship, but the total market can’t be over a few thousand whistles a year. As a rule the most expensive are usually sold directly by the maker to the end-user, often as a special order. The retail-market midrange whistles are going to musicians or musician wannabes (between the two categories, I guess I’ve covered most of C&F) . This can be direct from makers, by retailers like the Whistle Shop, or direct from one individual to another. These folks know what they’re worth and know that they can get just about that much on a resale.
Judging just by what I see in pet supply stores and pet food departments, the fish market is millions of people and hundreds of millions of fish. Despite all of our semi-joking about WhOA, there’s only a limited number of users and a finite and relatively small number of whistles they can consume - simply not enough volume to support an auction site such as you suggest.
Yes, we call it “eBay”. 
(Otherwise, what Chuck_Clark said, with the additional comments that the aquarium industry is HUGE, and since you can’t sell live animals on eBay, they’ve had to come up with something parallel.)