Adding my 2 cents FWIW ==
* ITA ... we all want those precious antiques to be worth a LOT, though often are not; being that you are connected to a pioneer settlement, it shouldn't be too hard for you to get an opinion as to whether there is any worth.
* quote with disclaimer/waiver ... good idea to CYA that an appraisal was recommended and they refused, also re the removal/disposal of the newspapers. That can be easily dealt with by presenting them with a quote of what's to be done, how you will do, and the agreed upon fees, inclusions/exclusions so there's no argument later, with the disclaimer as part of it
* wetting the newspapers may cause ink staining. The type of printing ink of that era came off on your hands. Some will remember reading the newspaper and getting ink all over their hands/arms or on their clothing. I have no idea as to whether with age it would have stabilized. Just beware ... you don't want to ruin it while in your trusting care.