Indeed, the source of the expression "one of the nine curses that plague mankind" appears to be Trall Dennison, in this article which appeared in The Scottish Antiquary, or, Northern Notes and Queries Vol. 5, No. 19 (1891). Note that in the article he does not explain what the other curses are, or mention them again.
Also in his much more detailed retelling of the folktale "Assipattle and the Stoor Worm", which appeared in Scottish Folk & Fairy Tales edited by George Douglas (of which you can find the scanned pages here) he makes no mention of the "nine curses".
Note also that Dennison did not claim the Stoor Worm to be the worst of the nine curses, but rather just one of them: the quoted passage in the Wikipedia page is from The Folklore of Orkney and Shetland by Ernest Marwick, who used Dennison as a source.
While it's entirely plausible that the nine curses were Dennison's invention, one should also take into account the likely Norse origin of the Stoor Worm myth, which is based on the similarities it shares with Jörmungandr. In the Norse mythological corpus (and in the Germanic corpus in general), similar references to the number nine are extremely common, as shown in this article by Joseph Hopkins and in the Wikipedia entry on Numbers in Norse mythology.
A very famous one is the reference to "nine worlds" in stanza 2 of the Völuspá. Just like Dennison's "nine curses", the "nine worlds" of Norse cosmology are not listed or expanded on in the corpus, and scholars are left wondering what they actually were (assuming there even was such a list).
A similar occurrence of the number nine in relation to the Stoor Worm appears in the aforementioned Dennison article a bit after the "nine curses". He writes:
Every Saturday morning at sunrise he yawned nine times.
This apparently irrelevant detail is quite reminiscent of analogous details appearing in the Norse corpus, like for example Thor taking nine steps before falling dead after his battle with Jörmungandr. Such details gain meaning in light of the significance the number nine held among the Norse.