A traditional bone glue. The type that has to be heated in the pot before use. Use sparingly.
When you use it to get that lovley flat finish and the sharp edges and corners etc. make up some small polished irons, apply the glue sparingly to the wood in a sort of spiders web and let it set.

Then apply the cloth ironing it on as you go. A normal house iron for most and a small flat iron you have made and polished for the tricky bits. This avoids wrinkles and any residule moisture or chemicals in the case that can attack polish or blueing.

Regards