Your best bet below 14th is Upstate on 1st Ave, but it’s not really a late-night shuck—on weeknights the raw bar often winds down between 10:30 and 11:00, so if you're rolling in after 11 you'll probably be too late. The Wren on Bowery keeps a small raw selection later than you'd expect, though it's more of a gastropub than a raw bar; I've gotten oysters there around 11:15 on a Thursday, but I'd call first because the selection can be fine one week and gone the next. Jeffrey's Grocery in the West Village has a proper raw bar setup and occasionally runs oysters late-ish at the bar, but it leans more 'neighborhood restaurant' than dive.
If you're willing to cross the river, Maison Premiere in Williamsburg is the obvious answer for late-night oysters in a serious bar setting, but it can turn into a scene and it's not exactly a sleeper. The Ten Bells on Broome does dollar oysters only during happy hour, not after 11, so don't chase that.
My rule for any place that's not a full seafood restaurant: look for the ice display and a shucker actually standing at it. If the station is cleaned and covered, skip the oysters and order something else. Late-night oysters at a dive are a risk I've taken, but I've also had a bad one after midnight and it ruined the next day. Ask when they came in and watch them open it. If the shucker can't answer, that's your answer.