Gee, guys, this isn't so hard, especially if you've raised kids:
"nappie" = "diaper" in the U.S.A. Diaper pins are exactly the same here as what you term nappie pins. Big safety pins may be used in lieu of diaper pins, of course - and they do indeed sometimes pop open and jab the baby. Diaper pins are safer, and your suggestion to include some is a good idea.
IME, diaper pins are also more robust than ordinary safety pins of equivalent size and are more suitable for pinning together thick layers than safety pins.
Blanket pins are altogether different than either of the above. We have a number of them around here somewhere in various sizes... but imagine my surprise when I went looking for a picture to embed here - there are vastly different styles of clasps/pins termed "blanket pin" - nothing like each other in form, and even some of different function. Mind boggling; I had no idea. Re-enactors probably have a totally different mental image of blanket pins than I do.
HTH,
Tom