Clemmensen Reduction
You're right about the side reaction (hydroxy-halogen exchange) in the case of cyclohexanols. It is nucleophilic substitution on a (secondary) alkanol under acidic conditions.

In the case of vanillin, your starting material, the situation is different. Under the conditions of the Clemmensen reaction, that is in the presence of (amalgamated) zinc and hydrochloric acid, a nucleophilic aromatic substitution can be ruled out.