But as it turns out, maybe Pikuach Fish is docheh Shabbos, at least a little bit.
- In this week's parsha (23:5) we learn the rule of פריקה, that the Torah obligates us to assist a man whose animal is overburdened by unloading it. Rashi there in Shabbos (קכח: ד"ה צער) suggests that our passuk is the source for the prohibition against צער בעלי חיים, causing pain to animals. Rashi, as do most Rishonim, paskens like Reb Akiva there that this is an issur de'oraysa. This is how the Rama (CM 272:9) paskens. Although Rashi says the source is Prika, other rishonim find many other sources for this din.
- The Rambam in מורה נבוכים ג-יז writes that the fact that the Malach rebuked Bilaam for striking his donkey (Bamidbar 22:32) shows that it is prohibited to hurt an animal for no reason. Reb Mordechai Carlbach in his Chavatzeles HaSharon points out that the Rambam apparently thinks that this prohibition is so logical and self-evident that it applies even to non-Jews.
- The Ramban and Chinuch (Mitzva 451) explain that the mitzvah of Shechita was given so that it will be killed in a manner which minimizes its pain. The same reasoning has been applied to אותו ואת בנו, לא תחרוש, and many other dinim.
- The Raavad and the Meiri מאירי בבא מציעא לב: derive this din from the commandment (Devarim 25:4) not to muzzle an ox while it is threshing.
- The Ritva בשיטה מקובצת בבא מציעא לב. ד"ה תדע just says it's a Halacha Le'Moshe Mi'Sinai.
So even assuming that fish feel pain, Pikuach Fish is still not docheh Shabbos. The most I could have done was call a gentile neighbor to help.