Air carrier Captain reported during landing rollout in poor weather conditions; the aircraft may have hydroplaned; skidded to a stop; and struck something while exiting the runway. Reporter stated that poor airport lighting and the use of reflectors instead of blue lights on the taxiway made it difficult to judge the amount of turn needed to join the taxiway.

Narrative

During landing rollout into ZZZ on Runway XXR with moderate thunderstorms with rain on the field in dark and very wet conditions with a moderate crosswind; the aircraft slid/skidded to a stop while on the Taxiway and possibly into the island between Taxiway XX high-speed exit in the Taxiway XY and possibly struck something; maybe a reflector. Due to significant maintenance being done on that side of the airport this area is unlit and only has the blue reflectors; not blue lights like at most airports; and because of the moderate rain falling at the time of landing and roll out; even with both the Captain and FO (First Officer) windshield wipers on low; the yellow reflective paint markings were difficult to discern/distinguish to aid me in the amount of turn that was going to be needed to join the Taxiway XZ that we were instructed to join upon exiting Runway XX right.The First Officer was Pilot flying for the landing and we had a positive transfer of controls at around 55 to 60 kts. He was on the Centerline when I received the airplane but I drifted right of Runway Centerline as I slowed the aircraft using the rudder pedals and differential braking; countering the right crosswind; trying to avoid the significant puddles of standing water on the Runway and Taxiway; trying to navigate the turn off for XXR at the high speed Taxiway XX.I slowed the aircraft to approximately 25 kts. before engaging the tiller and was braking for the right turn when the right main-gear brake antiskid engaged and the aircraft stopped at such an angle relative to the Runway/Taxiways that I had difficulty determining if we were on the Taxiway XX high-speed Taxiway; on the Taxiway XZ; or possibly on the edge of the concrete 'island 'area that divides Taxiway XX; XZ; and XY Taxiways. I could see the yellow Runway Edge Markings on the pavement in front of the nose and to the right; but I was not 100% clear if we'd slid/skid off the Runway/Taxiway and onto the 'shoulder' of the island.When the aircraft shuddered to stop I asked the First Officer if we were still on the Taxiway; and not actually in the island; and he said that he thought we were on the Taxiway and that we could continue on to Taxiway XZ. I was able to get the aircraft back toward the Centerline of Taxiway XX and make the right turn onto Taxiway XZ to continue to the gate without incident. I'm almost positive that we did not hit anything; but can only say with 90% certainty of this.The aircraft taxied with no abnormality to its rolling tendencies to the gate but I specifically asked for the FO to examine the right main gear for damage to the tires and gear assembly; just in case we had run off the Taxiway and unknowingly struck something in that island area. During postflight walk-around the First Officer found an area of what looks like the tire had skid and lightly flat spotted a line on the inner tread of the right main-gear outer tire; exposing five small areas of cord on the inner tread that were less than 3/4 of an inch long by 1/8 of an inch wide; each.In hindsight we should have had an airport operations vehicle come out the intersection we were at before moving the aircraft; regardless of what it would have done to the airport's operations during the very inclement weather in the immediate vicinity. A METAR was released one minute prior to our touchdown...[which included rain; thunderstorms; lightning; and wind]. The blue reflectors on that island need to be actual lit bulbs to aid in taxi off of the Runway. I should have stayed more on Centerline of the green lead-off lights instead of being so concerned about the puddles potentially causing a hydroplaning moment; that it appears we had; anyway.