Sending best wishes! I think scarf washing is pretty easy, and after the first try, is less scary!
I get everything set up before starting…several white, fluffy towels, a sweater drying rack, 2 plastic tubs/basins, and delicates wash (I use The Laundress). I place the drying rack wherever I'll be letting the scarf dry, and lay the towels flat in an area I use to place the wet scarf once washed, when I'll need to roll out the excess water. And finally, I place the two bins at a sink, and am ready to start. I fill one with cold water, with a squirt of the delicates wash, and I fill the second basin with cold water, no detergent. Then I submerge the scarf in the soapy water, and gently swish, keeping the scarf moving. Once clean, I move it to the basin with the clear water, and continue to swish. I empty the soapy water basin, and fill with clear, cold water. and move the scarf to the clear water basin, and continue back and forth using new, clear, cold water in each basin to swish and rinse, until no bubbles remain. I gently remove the wet scarf, holding a moment over bin to let some excess water drip away. I place the wet scarf on the white towels arranging it so that it's back to square, and as possible, not overlapping onto itself. I gently roll the scarf into the towels, then I unroll, and place on drying rack. Once somewhat dry, I iron, avoiding all hems, being care not to iron over them. Rolled hems will still be damp, so then I place back on the drying rack, to let it completely dry. Mousselines can be washed, but must be ironed while very wet. Otherwise the fabric gets crinkly (which can be remedied by rewetting, and ironing wet).
Good luck!