I agree with BriarRose - acrylic paint will change the hand of the silk too much. Especially as its a dance shawl?
I would be inclined to try discharging it - provided there is somewhere on the garment (seam or hem maybe?) that you can test out the colour remover to see what results you get. I have had good results with Jacquard's Discharge Paste/DeColourant on some commercially dyed silks. The results vary depending on the colour and what it was dyed with, so you definitely need to test it first. It's a paste so could be painted or stencilled on for an interesting design, you then iron it to remove the colour. Some colours won't discharge fully to white, some won't discharge at all.
You can also get a colour remover that you put the whole piece in and boil to remove the colour, called Thiox (Dharma Trading sell this as Dyehouse Colour Remover) however, you could get different results on the fringing to the silk, as there's a good chance the fringe was dyed with a different type of dye, and is probably a different fibre as well (not silk I assume).
My other thoughts are that a design stencilled on in gold or silver would be lovely. Rather than using gutta or acrylic paint I really like Jacquard's Lumiere fabric paint, it doesn't leave as much of a hand on the fabric and is much thinner than gutta. If you heat set it with the iron it will be wash fast. Also cheaper to cover a large area than metallic gutta.
In my mind I could see something like a gold damask design stencilled around the edges of the shawl might look nice, and only around the edges, wouldn't change the hand of the fabric too much?