Never heard of one shot delimited continuations; it sounds like an euphemism for "broken". Delimited continuations are functions; you can call them as many times as you like, with different arguments. They can call themselves recursively too.

Of course when I say "delimited continuation", I mean "delimited continuation" not "broken delimited continuation".

(If delimited continuations are used for simulating coroutines, it is my experience that they end up being called only once; each continuation invocation performs a time slice to the next yield. That's a particular simple use of continuations, not a type.)