We present a new syntactical proof that first-order Peano Arithmetic with Skolem axioms is conservative over Peano Arithmetic alone for arithmetical formulas. This result -- which shows that the Excluded Middle principle can be used to eliminate Skolem functions -- has been previously proved by other techniques, among them the epsilon substitution method and forcing. In this paper, we employ Interactive Realizability, a computational semantics for Peano Arithmetic which extends Kreisel's modified realizability to the classical case.