How to prepare vegetables for a sandwich that can last for several days in a fridge?
There’s a third option between storing the vegetables for a week and cutting them in the morning:

Cut just the amount you need for one morning the evening before. Storing overnight is not a safety issue (assuming basic principles like storing in the fridge are followed), and you still can “slap them on” as requested.

Another thought:
You describe cutting in the morning as too time-consuming, but my favorite tool in this context is a small cheapo vegetable slicer (like this one). I hold it right over the sandwich, shave a few slices of cucumber or similar right on it and am done. Thirty seconds, tops, including a quick rinse.

If you are interested in other toppings, I suggest you take a second look at the leftovers from yesterday’s dinner: Leafy greens like lettuce (sans dressing!) keep well for a few days and some roasted vegetables are also interesting: Either they are already spiced or a dash of lemon or mild vinegar plus an overnight stint in the fridge gives you a perfect sandwich vegetable - not unlike antipasti. Slice them right when you are packing them up, of course, for a grab-and-go sandwich preparation.