An experienced hand with slow-setting two-part epoxy (sometimes called araldite) is probably perferred over cyanoacrylate, but the water-thin super glue would be the best second choice.
For epoxy, you'd ensure the glue is mixed thoroughly, apply a thin coat to one surface, join the parts and clamp them in place, ignoring glue that squeezes out of the joint (it'll be easy to remove from the glossy glazed surface after it cures). Don't disturb the joint until the full curing time has passed, and keep it in a warm room (above 20 C). Once fully cured, the excess glue can be easily chipped off the glossy surface and carefully trimmed even with the glaze with a razor blade or similar thin, sharp blade.
For thin super glue, you'd join the parts dry, apply a minimum drop of glue at the join, and let it draw into the joint. If the joint area is large, you may need a second drop. Curing may take minutes, rather than seconds, on a non-porous material, but can be accelerated by breathing your moist, warm breath on the joint. Be careful not to use too much; it's difficult to remove cleanly, even from glossy surfaces, and there's a hazard of gluing your fingers to the statue.
The down side of this is that either glue will preclude a second try with the other, so it may be sensible to intentionally break a cheap item of the same material, to gain practice gluing.