In essence, what you need is a glamour - the *apperance* of change to all who may look at this, including yourself.
You can practise this in the mirror.
See a field around your hair, nebulous at first, that will filter the light reflection (which is exactly what hair dye does) to give the hair a different "colour".
Practise until the filter field (the glamour) becomes clear and you can *see* your hair colour changing. White is a good colour to practise with for beginners.
When you first start, the glamour collapses easily if your attention wanders; with practise, you can hold it steady for longer and also, you can fine-tune the colour you want. The last step is to have it be there on "automatic pilot" until you recall it/erase it with your will.
Once the glamour is steady, most others will *see* the new colour instead of the existing colour underneath. Psychics, witches and magicians should be able to see through the glamour, however, or at least notice an incongruency. A good strong glamour messes even with photographs and film to the degree that it is quite impossible to tell if its a glamour, or if there is really something there.
It's a handy thing, also works with hair colour, skin colour, and the advanced versions of this basic technique include invisibility to others, and shape shifting, even gender shifting.
Very useful all around for fun, pleasure, profit; sometimes it can be life saving even so it's worth practising that with a will.