I'm thinking about putting a few Polluted Delta in my deck to not only thin my deck, but also mitigate some of the life loss from Watery Grave. I know that shocklands come into play tapped regardless unless you pay the 2 life cost, but if I recall, you can crack a fetchland on your opponent's turn to put it into play tapped for only 1 life, and then untap it on your turn, correct? I don't know if it's even worth the effort, but I'm still curious if this works.

yes: no matter when it enters the battlefield, shocklands will untap during your next untap step as normal.

it's worth noting that this doesn't actually net you any additional mana compared to just searching for it tapped on your turn. the upside is flexibility: you can leave the delta up through their turn so that you can fetch an island or swamp if you need it, then if you didn't use it already, you can crack it for a tapped shockland during their end phase.