That would be a very good bit for a sensitive horse. There is no nutcracker action, the bit curves more around the jaw and the bars of the mouth and the cheek pieces are very comfortable. If you wanted something even more mild, then you would go with rubber(but that's hard to find with egg but cheek pieces). I like using metal bits more than rubber bits. They seem to communicate better (not by pulling!!!!!). I think rubber bits are good for young, sensitive horses but they don't last as long as metal bits. The bit in this picture has curved bars which is nicer on the horse's mouth too.
Nutcracker action doesn't really pinch the horses mouth like it says in the description because the bars of the mouth keep the bit too wide to pinch the tongue.Pinching only occurs, usually with a straight bar bit, between the tongue and the bar of the mouth. What happens with nutcracker action is where the bit is jointed, when it bends, it hits the horse's palette(which is sensitive). When riders yank a horse's mouth around and see-saw their mouth then it hurts the bars, the tongue, the teeth(if they pull hard and fast) and with single jointed bits it really hurts the palette. From the way you said your horse reacted to a single jointed bit, I think a double jointed bit would be better. The one in the link would be perfect.