I'm sure you've already come across North Carolina's info here: https://plants.ces.ncsu.edu/plants/clematis/

The principal toxic compound is 'protoanemonin' according to that source. I was able to find a few more sources on this compound produced by plants in Ranunculacea. I was able to find more information through Cornell about this compound here; https://poisonousplants.ansci.cornell.edu/toxicagents/ranunculoside.html. Clematis recta is listed as one of the plants that contain ranunculosides, the compound that eventually turns into protoanemonin.

Unfortunately, I was not able to find much information on the safety for ingestion by humans. There was a study conducted with one variety in rats, https://www.researchgate.net/publication/372359582_Toxicological_evaluation_of_aqueous_extracts_of_Clematis_hirsuta_and_Rhamnus_prinoides. I imagine that there is a lot of variability between species, and this is a bit outside of my expertise. I recommend deferring to medical professionals at poison control for more info. 

Since, I can't really weigh in on the safety of a certain plant for use in interaction with children, if you decide to use Clematis it might be a good opportunity to teach parents and adult visitors to the garden about the things that should be taught to children regarding having safe interactions with plants. Right across the parking lot is Monkshood, which is also pretty toxic. MSU has a nice article on this: https://www.canr.msu.edu/news/parents_and_children_gardening_together_safety_first. Like the article states, you may want to reach out to poison control, https://www.poison.org/, to see what they would advise if a child is having a reaction to the plant in question. That way you could decide if it's worth having that plant in the garden. It's probably best to avoid the plants on their poisonous plant list, https://www.poison.org/articles/plant#nonpoisonousplants, clematis is not on that list. Although, their non-toxic plant list is pretty short.

Here are some more resources related to children's gardens and plant toxicity from various extension agencies:

https://extension.illinois.edu/sites/default/files/plant_and_insect_safety_in_aaps_school_gardens.pdf

https://plants.ces.ncsu.edu/find_a_plant/?plant_type__id=15

https://poisonousplants.ansci.cornell.edu/comlist.html

If you're a bit deterred from using Clematis, some alternate plants that might serve in a similar capacity are:

Trumpet vine, Campsis radicans, is native and has low toxicity. There are newer cultivars that are a bit less vigorous and more manageable. https://plants.ces.ncsu.edu/plants/campsis-radicans/

Climbing hydrangea, Hydrangea anomala, https://plants.ces.ncsu.edu/plants/hydrangea-anomala/

Hardy kiwi vine, Actinidia arguta, edible, but not native, I bet between the kids and the volunteers there you could keep them in check though, https://plants.ces.ncsu.edu/plants/actinidia-arguta/

Grape vines could also be neat, but you may end up having issues with spotted lanternfly, this guide has some good northern varieties if interested https://extension.umn.edu/fruit/growing-grapes-home-garden#grape-varieties-for-northern-gardens-980960

I hope this helps!