Hi ksomom,
Post #2 here and the posts it links to has more information about safe, natural, organic, “chemical free”, and green mattresses and mattress materials that can help you sort through some of the marketing information and terminology that you will encounter in the industry and can help you differentiate between them and decide on the types of materials you are most comfortable having in your mattress and help you answer “how safe is safe enough for me”. These types of issues are complex and are generally specific to each person and their individual sensitivities, circumstances, and specific criteria.
Once you have decided on the materials that you would be comfortable with … post #2 here has some guidelines and links to the better forum posts and topics about mattresses and children and includes more information about some of the better options that are available as well.
This topic may also be well worth reading because they were also looking for a top bunk mattress under 6" as well.
Post #2 here includes a link to a list of the better options and possibilities I’m aware of in the Hawaiian Islands and links to some feedback from other members there as well. You would need to check with them though to find out whether any of them sell a child"s mattress that would meet your “safety” criteria.
Phoenix