Protecting a missile-refitted Lion from gun blast

Could a modernized Lion class carry close-in weapons and Sea Dart or Sea Cat without its main-gun blast wrecking the electronics?

Close-in guns and perhaps Sea Slug were plausible, but Sea Dart would need an aft position and extensive shock isolation.

Goalkeeper mounts could plausibly coexist with the Lion class's heavy guns, but the missile installation would be harder. Sea Slug was comparatively robust for this environment. Sea Dart would need to sit aft and have its machinery isolated on shock-absorbing rafts because the main battery's blast could damage sensitive electronics. Adding modern weapons to a battleship requires deck space, shock protection, and blast protection.