This, unsurprisingly, is also related to mermaids.
Spearguns using rubber bands and the like are popular underwater weapons, so slingshots would be useful to mermaids. The problem is, these require(?) vulcanized rubber, which was invented in the 19th century.
I'm wondering if there is any way you could get this, or a similar material sooner, or stumble onto it someway. This may be more plausible than it sounds.
Invention of Vulcanized Rubber
The legend goes that Goodyear, who was not college trained, accidentally spilt rubber and sulfur onto a hot stove, and noticed it become a strong material. He claimed it was no such thing, but if it is technically possible that could happen, any alchemist messing with sulfur and rubber might discover this, and mermaids may gain access to such an invention.
But, I really need a more expert opinion on this, to know if it's really plausible, or how it could come about. As a side note, rubber use in Europe appears to have started in the 18th century, not sure why there wasn't any sooner.
Effects on the Ancient World?
There is also, as a side question, how this would affect the ancient world if vulcanized rubber (and rubber trees) were discovered. But this is less important to me, as I mostly want to know about its plausibility for it to happen.