Electrospun fiber mats loaded with therapeutics have gained considerable attention as a versatile tool in the biomedical field. While these bandages are largely based on fast-dissolving polymers to release the cargo, stimuli-responsive fiber mats have the advantages of providing a timely and spatially controlled drug delivery platform, which can be refilled and reused several times. These benefits make electrospun fiber patches original platforms for painless and convenient on-demand hormone release. Because of the high need of more convenient and non-invasive methods for delivering insulin, a hormone that is currently used to treat hundred million people with diabetes worldwide, we have investigated the tremendous potential of reduced graphene oxide modified poly(acrylic acid) based fiber mats as an original platform for buccal and corneal insulin delivery on-demand. The PAA@rGO hydrogel-like fibers rendered water-insoluble by incorporating β-cyclodextrin, followed by thermal cross-linking, which showed adequate tensile strength along with high adsorption capacity of insulin at pH 7 and good recyclability. The fiber mats maintained good fibrous morphology and high loading efficiency even after five loading–release cycles. The mucoadhesive nature of the fibers allowed their application for insulin delivery via the eye cornea and the buccal mouth lining, as evidenced in ex vivo studies. Insulin loaded PAA@rGO hydrogel-like fibers showed an insulin flux via buccal lining of pigs of 16.6 ± 2.9 μg cm–2 h–1 and 24.3 ± 3.1 μg cm–2 h–1 for porcine cornea. Testing on healthy adult volunteers confirmed the excellent, mucoadhesive nature of the bandage, with three out of six volunteers feeling completely comfortable (note 8.3) while wearing the patches in the buccal cavity.