Political status determines who provides the navy

If Britain had not lost Malaya, would Malaysia's and Singapore's navies still have emerged?

Probably, because imperial rule would still be expected to give way to Commonwealth independence, and independent states require their own naval institutions.

The 1942 military disaster was separate from the longer process of imperial dissolution. Even without the fall of Malaya and Singapore, the empire would likely become a Commonwealth of independent states. Their navies would arise from sovereignty and local defence responsibilities rather than Britain's wartime defeat alone.