Advice on best way to recolour this image

If you’re wanting to recolour the beanie into multiple shades, one effective way (that gives you more precision than global Hue/Saturation) is to create a Hue/Saturation adjustment layer with a mask. That way, you can paint on the mask to isolate only the beanie area and then tweak each colour separately. Another option is to use Select > Color Range to grab just the knitted areas you want to change, then apply a Solid Color Fill Layer set to Color or Overlay blend mode. This keeps the fabric texture intact while letting you try out different shades quickly. If you need three completely different colour versions (say, blue, red, green), duplicating the layer and applying different adjustment layers to each copy works well—you can then export each version individually.

I came here to say what @Derek Cross said, but I'll add that the Color Balance sliders might also be of use. Go Image>Adjustments>Color Balance