Myocardial remodeling is an inevitable risk factor for cardiac arrhythmias and can potentially be corrected with cell therapy. Although the generation of cardiac cells ex vivo is possible, specific approaches to cell replacement therapy remain unclear. On the one hand, adhesive myocyte cells must be viable and conjugated with the electromechanical syncytium of the recipient tissue, which is unattainable without an external scaffold substrate. On the other hand, the outer scaffold may hinder cell delivery, for example, making intramyocardial injection difficult. To resolve this contradiction, we developed molecular vehicles that combine a wrapped (rather than outer) polymer scaffold that is enveloped by the cell and provides excitability restoration (lost when cells were harvested) before engraftment. It also provides a coating with human fibronectin, which initiates the process of graft adhesion into the recipient tissue and can carry fluorescent markers for the external control of the non-invasive cell position. In this work, we used a type of scaffold that allowed us to use the advantages of a scaffold-free cell suspension for cell delivery. Fragmented nanofibers (0.85 µm ± 0.18 µm in diameter) with fluorescent labels were used, with solitary cells seeded on them. Cell implantation experiments were performed in vivo. The proposed molecular vehicles made it possible to establish rapid (30 min) electromechanical contact between excitable grafts and the recipient heart. Excitable grafts were visualized with optical mapping on a rat heart with Langendorff perfusion at a 0.72 ± 0.32 Hz heart rate. Thus, the pre-restored grafts’ excitability (with the help of a wrapped polymer scaffold) allowed rapid electromechanical coupling with the recipient tissue. This information could provide a basis for the reduction of engraftment arrhythmias in the first days after cell therapy.