Religion. There's tons of swears that call The/A god's name in vain, or even just parts of said deity. "Odon's Beard", "God's Body" (which morphed into "Odd's Bodkins"), "Go to Hell/ The Devil", etc. One of my favorites from Spartacus "Great Merciful Bloodstained Gods!"
Many curses and swears are connected to specific unpleasant events. In a sci-fi series I enjoy, one of the foulest swear words around is "whistle", referencing the sound of escaping air that a micrometeorite puncture would cause in a space suit. References to evil or incompetent leaders might serve well, as in Star Trek's "Herbert". King William the Large might be so universally despised that calling someone a "Bill's Boy" is on par with suggesting one of your parents was a farm animal.
While sexual taboos aren't as big a thing in your world, there will absolutely be rude terms for bodily functions. There will be a plethora of words for poo, pee, and the various reproductive fluids and equipment, varying from "patently adorable" ("Are you referring to number one, or cockee-doody?") to the kind of words that'll get you excommunicated.
Sometimes getting the etymology down isn't as big a deal as just getting the sound right. So many sci-fi curses sound sort of like "real" ones, like Smeg, Frak and Sprokk/Drokk (from the Legion of Superheroes comic). We never learn their origins, but we know immediately they're "sour language" (as my kid calls them) Single syllables, with a solid consonant in them, something that makes you feel better after your stub your toe.
There was a great episode of the cartoon Recess where the gang decides to create a new curse word, one they can use without getting in trouble. They settle on "whomps", as in "This really whomps". It's so successful, a school administrator hears it an tries to get it banned.