Q.Child Friendly Climbing Plants
I have a garden arbor that is only 1/4 covered by a small purple flower plant. I would like to plant another climber so the arbor is completed covered. I would like it to flowering, pink or white preferably, but it must be safe for children – non toxic to eat or touch and no thorns.

I personally have Clematis planted on the sides of my potting shed, which was previously my daughters play house.
There are many varieties available that would bring you the whites or pinks you are wanting for your garden.
Teaching your young gardeners that flowers are beautiful to look at and smell but not taste is their first gardening lesson.
Here are a couple of articles that may help you get started.
https://www.gardeningknowhow.com/ornamental/vines/ovgen/growing-perennial-vines.htm
https://www.gardeningknowhow.com/ornamental/vines/clematis/growing-clematis.htm