Extract payload from dump

Hi, I dumped some network traffic using wireshark and I need to extract the actual payload of the packets in a new file, i. e. to get rid of link layer, internet layer, transport layer headers and save the application data. In Wireshark, there's this "follow stream" function, but I need it to be scriptable and non-interactive since there's gigabytes of dumps in hundreds of files. Does anyone have an idea how I could accomplish this? Thanks in advance!