Westy:

No sir, a spinner is not required.

You can use the nut and washer set as it is without a spinner, so long as the prop hub thickness is great enough to tighten the nuts. As you show in the bottom right picture this will be around 3/4" or 19mm total. That particular set is intended for use with a spinner having a thick back plate, there's a different set that does not fit into the prop hub allowing a thinner prop.

If the prop hub is too thin for that you can alternately get a thick flat washer that is a close fit on the crankshaft allowing the end of the larger nut to press directly on it, then use the locking nut to seat inside the larger nut in the normal manner.

Picture shows your set on the left, the conventional adapter it on the right. Both available from Tru-Turn. Click [link=http://www.truturn.com/cgi-bin/store/agora.cgi?exact_match=on&p_id=tt0823a&ppinc=adaptp recision]here[/link] to see them.

Bill.