String instrument repair people depend upon violins and such being put together with hide glue. The instruments have to be taken apart for repairs, so the joints have to be temporary, though maybe not opened up for 100 years or so. The opening process is done very carefully with a thin blade. Centuries of experience have shown that hide glue joints can be broken without damaging the wood. Never stick a good string instrument together with epoxy or Elmers or super glue. Same goes for good antique furniture.
In the case you describe, hide glue and a heated palette knife might be appropriate to prevent damage to the carved parts. Or, use hide glue to attach the wood to a metal block and heat the metal when ready to remove the wood. Hide glue is heated in a double boiler to use, so it can be melted to separate a joint.
Watch repair people use a similar technique, but use stick shellac to attach parts to a metal holder. Shellac melts easily and can be removed with alcohol. Colored stick shellac is often used to patch dings and cracks in furniture, but is not for use as wood glue. Liquid shellac is stick or flake shellac dissolved in alcohol so that it can be applied with a brush.