In the clinical management of solid tumors, the possibility to successfully couple the regeneration of injured tissues with the elimination of residual tumor cells left after surgery could open doors to new therapeutic strategies. In this work, we present a composite hydrogel–electrospun nanofiber scaffold, showing a modular architecture for the delivery of two pharmaceutics with distinct release profiles, that is potentially suitable for local therapy and post-surgical treatment of solid soft tumors. The composite was obtained by coupling gelatin hydrogels to poly(ethylene oxide)/poly(butylene terephthalate) block copolymer nanofibers. Results of the scaffolds’ characterization, together with the analysis of gelatin and drug release kinetics, displayed the possibility to modulate the device architecture to control the release kinetics of the drugs, also providing evidence of their activity. In vitro analyses were also performed using a human epithelioid sarcoma cell line. Furthermore, publicly available expression datasets were interrogated. Confocal imaging showcased the nontoxicity of these devices in vitro. ELISA assays confirmed a modulation of IL-10 inflammation-related cytokine supporting the role of this device in tissue repair. In silico analysis confirmed the role of IL-10 in solid tumors including 262 patients affected by sarcoma as a negative prognostic marker for overall survival. In conclusion, the developed modular composite device may provide a key-enabling technology for the treatment of soft tissue sarcoma.