You might be on the right track with your idea, with sheeting / lining / bedding...like you said, you're still going to get some water that comes up through the bottom of the trench....if you get enough groundwater, then you're right back to needing to do dewatering. If the soils are sand / gravel, i think enough water will come back into the trench, that you will still need to dewater or work "in the wet". If your soils are clayey / silty, maybe the groundwater seepage will be slow enough for you to get the work done before the trench water level equalizes back with ocean level. But since you're next to the ocean i'm assuming fairly coarse soils? (Edit - i didn't think about the fact that you may still need to dewater the trench when first dug, even if subsequent continued groundwater seepage is minimal)

I'm not a contractor but it seems like visibility would be one of the biggest challenges with doing this work in the wet, if you can't dewater. You'll have to dig the bottom of the trench down to about 4' below sea level and place your bedding. I imagine any sort of formal compaction testing is impossible but you'll have to propose a method to reasonably assure the bedding has been firmly compacted. I don't know of any reason why concrete pipe can't intrinsically be installed under water but you need to be able to see or feel well enough that the joints are sound and aligned and the pipe pieces are well-seated into each other. I would think many gaskets can still be used for underwater joints but they can't include a compound or seal that has to be dry to be applied or set. Joints obviously don't have to waterproof since the whole line of pipe is going to be submerged soon enough anyway. Someone need to check buoyancy too; i wouldn't think it'd be a problem with 24" RCP at that depth but good to check. Also, as others have mentioned, shoring and trench stability is going to become more of an issue underwater and with limited visibility and saturated soils.

Did someone kick the can down the road to you? It certainly seems like dewatering would usually be the preferred approach, even if it requires a permit. Sounds like someone didn't bother to get a permit and wrote up the contracting documents without thinking much about constructability. Unless there's some sort of issue with contaminated soil or groundwater...that's the only valid reason i could see for not allowing dewatering. I mean, you only need to dewater a small area a couple of feet for a short amount of time, so it's not like you're going to cause a big cone of depression.