That, to me, looks just like the one in my link at 11:36. I use a spanner with long jaws and hold it on the tap handle like the man in the video did with the pliers; I find a spanner easier.
Incidentally, you can undo the nut which the man was heating with the candle - it will not allow water to leak past it but it will allow you to get the WD40 in more easily. Hitting the handle with a hammer frightens me; just rocking the handle is far less likely to cause damage. I would also add that whenever I open a stop-cock to allow the water to flow again, I close it again by a small amount (1/4 turn, say) which means when it gets stuck again you can rock it with the spanner without the danger of damaging anything.