Dave W wrote:

All right, don't use strings...

Sorry to have been so long responding to this. If hanging from above is out
(which I think it is) then the three main options seem to be an inflated
figure, a dummy built around a collapsible internal structure of some kind,
and a hanging puppet-like construction supported from behind by a rod or
similar protruding through a curtain.

Clearly a bit of experimentation is called for.

Thanks to you and everyone for the thoughts.