If the process described below does not suit you, dry cleaning will be perfect to take care of your shawl.
HOW TO WASH YOUR SHAWL SAFELY:
Dissolve a little quantity of mild detergent - like gentle shampoo or woolen soap - with cold or lukewarm water (at 30 °C /86 °F maximum)
Submerge the shawl in the water and move it gently for a few minutes. Do not use fabric softener and rinse the shawl very well by running cool water through it to remove the soap.
You can then take out extra water by applying gentle pressure. NEVER RING, NEVER TWIST.
Remove the excess water by rolling the shawl in a clean towel.
Preferably lay it flat. If not possible, fold it once or twice to prevent the fibres to be stretched too much and hang it on the clothes line in avoiding direct sun or any proximity to heat sources.
Once dry, if available, the shawl can be steamed which will fluff the fibres. Otherwise, it can be ironed with a warm iron.