Any PVA glue intended for schools or children should be safe, as they're the same thing as Elmer's glue. Elmer's glue is the most common brand of children's PVA glue in the US, which is why it's commonly recommended. For more structural things or anything that needs to support weight, you would probably need a PVA wood glue though, like Ponal. I'm not sure about the Collall one linked. This one says it's non-toxic:
Amazon.co.uk.