Pascalemod,
Hank is generally correct in a broad view of the FLETCHER class configurations from 1950 to 1972 while in USN service. But, you are asking about USS WADLEIGH (DD-689) "during the Korean War". I have to ask for what period during the KW are you wanting to model this ship?
When the FLETCHERS were mobilized from mothballs at the start of the KW and for that matter, what became the more intense Cold War, the plans for upgrading them evolved over their service life. The authorized upgrades changed configuration appearances and depending on when a destroyer was overhauled or retired, would last for only a short while or remain until the ship was scrapped.
Initially 41 out of the 82 (all Square-Bridge units) "Fleet Destroyer" configured FLETCHERS and recommissioned in the mobilization (18 other FLETCHERS were being converted to the ASW DDE configuration), were authorized to be upgraded with three twin RFG mounts in place of one 5-in/38 mount and all their 40-mm guns. Due to cost overruns, only 39 FLETCHERS while in USN SERVICE were were upgraded with 3-in RFG mounts in 1950-54 period. This modification became known as the "4-Gun FLETCHERS". USS WADLEIGH was one of those units, being so modified in early 1953 (corrected) at BosNY. The remaining FLETCHERS in service, were modified to what was known as the "5-Gun FLETCHERS", that basically was the late WWII Anti-Kamikaze Mod with two quad 40-mm mounts, also replacing the forward twin 40-mm mounts with two Hedgehogs and "generally" new radars (most on tripod foremasts) and sensors.
Prior to that upgrade, she was assigned to the Atlantic Fleet and didn't see service in the Southeast Asia area until, AFTER she was upgraded and a year of training, in May-November 1953 timeframe. Actually she didn't see service off Korea, but rather off Taiwan during a crisis period with China, before returning to Atlantic Fleet service. She went on to serve in the USN in the Atlantic Fleet until 1962 and saw additional modifications to her configuration, primarily upgraded electronics.
So to fully answer your question, I need to know just when, timeframe, you which to model USS WADLEIGH?
Early recommissioning configuration for WADLEIGH has her still in a basic WWII configuration that could be best matched by the Trumpeter "THE SULLIVANS" 1/350 kit. This image shows her during March 1952 when she was used in a movie.

After her 3-in RFG upgrade, she had the standard configuration as authorized at the time. Note that she has the SPS-6C radar and minimal ECM suite at this time. The ECM suite and her ASW armament would be upgraded in late 1950s.

AS for upgrading a 1/350 scale kit to a 1950's configuration, the Trumpeter 1/350 scale THE SULLIVANS kit is likely your best option. The Tamiya 1/350 FLETCHER kit would require more work with an aftermarket 3-D printed Square-Bridge form Model Monkey beside all the other components. There are aftermarket twin 3-in RFG mounts, Mk 56 GFCS, and Mk 63 GFCS available. But, you will need to scratch build the revisions to the midships deckhouse and aft deckhouse along with the "tubs" required for the RFG mounts. Model Monkey has "generic" twin 3-in RFG "tubs" that appear to be close enough when modified for a 4-Gun FLETCHER build.
At one time there "WAS" a 4-Gun conversion set for Tamiya 1/350 kit in resin. But, it had a LOT OF ERRORS and is no longer available in any case.
This is exactly the photo I've been looking for! My dad served on the Wadleigh in 1957. I still need to find a top view image.