Were any escorts designed with only Hedgehog or Squid and light anti-aircraft weapons, without a deck gun?
Short answerNo; escorts still needed a gun for surfaced submarines and encounters with torpedo boats such as German Schnellboote.
NotesA surfaced submarine could force an escort into a gun action, and a design armed only with Hedgehog or Squid would be unable to answer effectively. Flower-class corvettes also encountered German Schnellboote in the Channel, where a deck gun and lighter weapons had uses wholly separate from attacking a submerged contact. The mixed threat explains why specialised anti-submarine ships retained conventional surface armament.