You should not use any body else's razor for your personal usage. There can be many skin conditions that can get transmitted. Kindly refrain from such [ractices. Fungal infection is becoming an increasing problem due to misdiagnosis and wrong treatment with OTC medications. To add to the problem, many combination tubes are easily available in market and there is no regulation on the sale. They make the fungal infection a permanent problem though it may provide temporary relief.

Greetings. Don't worry, shaving with your father's razor and because he has white hair doesn't mean you'll get white hair or fungal infection. In case your father has fungal infection then a theoretical possibility exists. But don't worry. However, it's advisable that you use a personal Razor for yourself at all times. Take care.