Hiya!Nice sewing box I'd look for fabric cleaner, the sort that you foam up and then apply the foam with a sponge,leave a bit,then sponge off? Spect I'd be looking in the s'market aisle that has leather cleaner etc. I wouldn't want to get it too wet.
Original Stardrops in warm water - dunk a cloth in it and wring out so it's just damp. Then use it to gently clean the box. Rinse the cloth out in the water periodically. The key is not to let the item you are cleaning get too wet.