I’d always been taught to use the side of my finger tips too. They always seam slightly thiner than the “Pads”.
I also seam to remember using blood from a graze knee, elbow, or other scab you can’t seam to stop picking at.
Rubbing your hands together to warm them up also can help,
Also I spouse you could try anything to increasing your heat rate ie increase the speed the blood is flowing, or increasing your blood pressure…….. (Sudden Shocks, Surprises, Exercise and the like but that sounds like all the standard methods to cure the hiccups)
I’ve also find that high blood sugar blood flows more easily!