The demand for lightweight materials, such as fiber-reinforced plastics (FRP), is constantly growing. However, current FRP production mostly relies on expensive molds representing the final part geometry, which is not economical for prototyping or highly individualized products, such as in the medical or sporting goods sector. Therefore, inspired by incremental sheet metal forming, we conduct a systematic functional analysis on new processing methods for shaping woven FRP without the use of molds. Considering different material combinations, such as dry fabric with thermoset resin, thermoset prepreg, thermoplastic commingled yarn weave and organo sheets, we propose potential technical implementations of novel dieless forming techniques, making use of simple robot-guided standard tools, such as hemispherical tool tips or rollers. Feasibility of selected approaches is investigated in basic practical experiments with handheld tools. Results show that the main challenge of dieless local forming, the conservation of already formed shapes while allowing drapability of remaining areas, is best fulfilled by local impregnation, consolidation and solidification of commingled yarn fabric, as well as concurrent forming of prepreg and metal wire mesh support material. Further research is proposed to improve part quality.