By mid-1944, the IJN was truly facing a crisis and was likely well past the point of no-return. The defeats of 1942, and the extended Solomons Island campaign had badly ground down its forces. The majority of 1943 was spent attempting to marshall new resources, and--most importantly--rebuild the striking power of its carrier air groups, which had suffered heavy losses during the carrier battles of 1942. When the United States continued its Central Pacific campaign by striking at the Marianas Island--including the key island of Saipan--that constituted the inner perimeter of Japan's defenses, the IJN committed its assets in an attempt to fight the Decisive Battle it had long been preparing for.

The resulting battle was indeed rather decisive, though not in the way Japan had hoped. Japanese attempts to destroy the US fleet attacking the Marianas resulted in the Battle of the Phillippine Sea, which saw what was left of Japan's naval air power utterly shattered, combined with the loss of threefleet carriers, the veteran Shoukaku, the converted Hiyou, and the brand new Taihou. Thus, by the time the Marines had landed on Peleliu Island, the IJN had already comitted the majority of its remaining forces (including its carrier forces) to a major fleet battle that had seen them defeated. The remaining Japanese surface units could not operate freely in the Central Pacific.

Unlike Guadalcanal, where American aircraft were mostly limited to the airbase on Guadalcanal, and the Japanese had their own powerful base nearby at Rabaul, Japanese surface ships would not have been able to close to bombardment range at night, and withdraw to the safety of Japanese air cover by dawn. Moreover, the powerful American Fast Carrier Task Force controlled the seas, again unlike Guadalalcanal where the rough partiy of ship strength meant that neither side had complete control of the sea lanes off the island. Had the Japanese attempted the same tactic of night bombardments, the bombardment force would no doubt have been either intercepted on its way in or out by the roving American carrier fleet. Moreover, such a bombardment force would have had no air cover, since the available Japanes naval aviation forces had been severely damaged at the Battle of the Phillippine Sea but a few months prior.

So to sum up: no. There were no surface actions directly off of Peleliu, at least not ones at all similar to the major clashes off of Guadalcanal.

Hope this helps, and feel free to ask any follow ups!