I'd have a go at steaming the scratches out. A soldering iron on a piece of damp cotton over the scratches keeps the steam local. It may not completely fix it, but it should lessen the severity so that any sanding needed is much less. Just keep the cotton damp, not wet. You may need to do it a few times, so apply some steam, then stop and have a look. Repeat three or four times if necessary.
Let the veneer dry overnight before attempting to sand.