Chlidonias is 100% correct on all accounts. The number of people who've told me they can't open their mouths wide, (or they have small fangs, or they don't have the power to break the skin) would be in the several dozens.
They are more venomous than any land snake, but the two species found in Niue are extremely placid and inoffensive. They are curious, and as humans often stir up the substrate, they may follow to see if anything worth eating has been disturbed.
The animal in the photo above was content to be handled gently for a few moments before swimming off.
I have actually read in many places that Australia's turtle-headed sea snake Emydocephalus annulatus is non-venomous (it feeds on fish eggs), but I have also read that it has a weak venom (as opposed to none at all). I'm not sure on which is true.