Yeah, none of the MC exploits for water breathing work here.
If I don't feel like using ladders (lately I am overloaded with sticks anyway, so I use them) then I pour a bucket of water at the top, dig down til I am almost out of air, and then dig a 1x1x2 and stand in it to top up air and then continue digging.
For a cave you could dig 1 block overhead and then swim up; as long as your head is out of water you can get air.