Boiling it will likely destroy the ornament. The anthill idea will work, but...you need to have an anthill handy, and a lot of patience.
I think your best bet will be to try a technique that many taxidermists use to clean out all soft tissue from animal skulls, to create bleached trophies that are referred to as "Euro" mounts. Essentially, it involves submerging the object in a bucket of water and then keeping the water warm and allowing the meat to rot away. Changing the water periodically helps, but make no mistake: this is going to stink. If you live in a rural area, or have a large yard, you can make it work. Apartment dwellers need not apply. A few weeks should be sufficient to break down the soft tissue enough for a hose to rinse it out. It's possible that the skeleton may become a permanent addition to the ornament; a piece of "hidden" decor.
I think your best bet will be to try a technique that many taxidermists use to clean out all soft tissue from animal skulls, to create bleached trophies that are referred to as "Euro" mounts. Essentially, it involves submerging the object in a bucket of water and then keeping the water warm and allowing the meat to rot away. Changing the water periodically helps, but make no mistake: this is going to stink. If you live in a rural area, or have a large yard, you can make it work. Apartment dwellers need not apply. A few weeks should be sufficient to break down the soft tissue enough for a hose to rinse it out. It's possible that the skeleton may become a permanent addition to the ornament; a piece of "hidden" decor.

