Since this is very much a what if question, I'll throw something else in the mix between the Kongo/Haruna and Repulse/Prince of Wales. The other large warship that was to accompany the two British vessels as part of Force 'Z' was the carrier HMS Indomitable, newly commissioned and sent to Singapore via the Caribbean, where, on entry to the harbour at Kingston Jamaica, she struck the Palisadoes Reef at the harbour bar, which rendered her inoperative; she was sent to the USA for repairs, so missed the sinking of the two ships by the Japanese.
If Indom was there at the time that the Repulse and Prince were attacked, it would have added another element to the mix, particularly if the Japanese battleships were present (according to my copy of Siegfried Breyer's book Battleships and battlecruisers 1905 - 1970; "The fitting of torpedo bulges reduced their speed and from 1930 onwards they are therefore classified as senkan = battleships" - pedant
).
On an historical note, Singapore wasn't the last time that Indomitable escaped a probable fate; the ship was sent to Ceylon after her repairs and in early April 1942 was sent out on patrol to intercept a Japanese carrier group led by Adm Chuichi Nagumo and comprising five carriers, four fast battleships, cruisers and destroyers. Her torpedo bombers were readied, but the ship was not sent after the Japanese. She missed the bombing of Colombo on the 5th April by Japanese carrier aircraft. On that day the cruisers Cornwall and Dorsetshire were sunk.
A few days later the carrier Hermes and destroyer Vampire were also sunk by Nagumo's aircraft. I read an account by a crewmember of the Indomitable once and the guy couldn't understand why they didn't intercept the Japanese, although it turned out that the Japanese task force was far superior in numerical size than the British ships in the region, which also included the battleship Warspite and carrier Formidable. According to this guy's account, Adm Somerville with held the British carrier because he wanted to prevent the inevitable.
Sir John Somerville was commander of the Eastern Fleet, which comprised Indom, the carrier Formidable and the battleship Warspite had Singapore as his base for awhile, but left once the situation became untenable, although at that time his ships were elsewhere, both Formidable and Warspite had undergone repairs in the USA after bomb damage in the Mediterranean and were sent to the Eastern Fleet in February and March '42. So had the Warspite and Formidable not been damaged in the Med, they would have probably ended up in Singapore too. Just a thought.