Do any other Prime Weaponskills other than Origin have a hidden effect?
The drain/apsir effect on Origin isn't a hidden effect, its just how the WS operates.
Even Catastrophe lists the drain effect in the WS's description. Relics did have "hidden" effects such as Catastrophe giving haste. It was only "hidden" on the lvl 75 version. After that, they were listed as "Aftermath:" effects.
Cata and Origin are pretty unique with the drain. All other primes are just strictly damage only. However there are other WS's that give effects such as Guillotine and Tachi:Gekko having a silence effect. Plenty of Stun WS's also.