You could not remove the spoiler completely, but you could make it go unnoticed for a slightly unattentive viewer by removing the obvious pieces and transforming the rest into hints. However, I think the lowering of the mask is one of the more powerful scenes in the film, so I would keep it in my own edit.

I would keep the birth but replace the sound with a voice-over of Obi-Wan, Yoda and Bail if a suitable dialogue can be found. Perhaps also cut the shots of Padmé's face as she names the babies.

I would also cut or shorten the Vader-naming, only because it is so hideous.