Welcome Susan!
I like the idea... I've always imagined finding a twig of some sort as a handle, or just perservering with the blade without a handle.... do you know how the clay stands up to humid conditions/ getting dunked in water?

As for clay type products that don't need baking, there is a substance used by modellers called 'green stuff' which is bought as a strip of yellow and blue 'stuff'. When the two are mixed together they become green (hence the name), and are used to model detail on to metal and plastic minitures. The stuff sets without heating in about 24 hours, if I recall correctly. It is however hard work on the fingers to get the yellow and blue stuff to mix evenly - I wouldn't want to do it in a survival situation.

All the info you could ever want on it is available here: green stuff