OK, a bit of casual googling has found a few references to Cotswold Morris handkerchiefs being called "wavers". However the term seems to be more usually applied to the decorated sticks used by North West sides.

I would still disagree with Diane's original implication that "wavers" is the correct term, rather than handkerchiefs. I would be interested to know when the term first started to be used. If it's favoured by the Morris Federation I wonder if it's because women don't have suitable handkerchiefs :-)

Cecil Sharp's Morris Book calls them "handkerchiefs".