I walked away quite frustrated from the bench after looking at the results. Quite some bleeding of the orange paint and, what I thought to be, chipping of the white paint.
Returning to the bench and having a better look at how to get it solved, I noticed that the darker marks on the white paint was not chipped paint but remains of the glue from the masking tape. Using a damped cloth, several rounds, I was able to remove the glue and as a bonus this worked also for removing the bleeded orange. You can imagine that this made my day and also that of my daughter, she was clearly not happy with the first outcome 🙂