Could World War II technology build a guided-missile ship?

A destroyer-sized ship could carry enlarged radio-guided weapons derived from the Hs 293, but their short reach and manual guidance would make the vessel far less useful than a 1950s or 1960s missile combatant.

Question

Could World War II technology produce a guided-missile ship like those of the 1950s or 1960s?

Short answer

Only in a crude sense: a destroyer could launch a few enlarged radio-guided weapons, but their range, guidance, and shipboard integration would not equal a postwar missile combatant.

Notes

A destroyer-sized hull could theoretically carry three or four launchers for enlarged radio-guided weapons derived from the Hs 293. Operators aboard the ship would guide each missile toward its target. The objection is that the vessel would have a weapon with a reach comparable to a motor torpedo boat's while presenting a larger, less survivable target. It might launch within enemy gun range and be destroyed before completing guidance. That crude late-war possibility falls well short of the guided-missile combat system implied by a 1950s or 1960s ship.