Why would I as a sole trader need a health and safety policy? The only employee I have is me so the only person who needs to read and adhere to it is me.
That wouldn't be a health and safety policy, that would be risk assessments and method statements if it covers specific tasks, a health and safety policy sets out a company's general attitude/approach to health and safety, not the specific mechanisms by which it is applied.
Then don't have one, but this thread is an example of why you might like to have one.
Do I need one? No because the company only has two employees me and A. N. Other. Do I have one? Yes, because well... it's easy to produce one using the HSE resources, so why wouldn't you?