Any particular reason you don't want plastic in your tank? You say plastic, but most aquarium ornaments are made of resin as plastic floats.
Something like that made of stone certainly isn't going to come cheaply.
Unless you go for the expensive one, resin ones are usually still hollow, but a stone one would cost a bomb. An option could be to drill some holes in the back for water to escape if there aren't any as part of the design, then setting an air stone to run underneath/inside it. Even if you just had it on one minute a day, it'd be enough to keep circulation and stop the water going stagnant inside.
btw is there a way to test to see if the statue is safe to put in the aquarime.