Quantum confinement permits the existence of multiple terahertz magnon modes in atomically engineered ultrathin magnetic films and multilayers. By means of spin-polarized high-resolution electron energy-loss spectroscopy, we report on the direct experimental detection of all exchange-dominated terahertz confined magnon modes in a 3 ML Co film. We demonstrate that, by tuning the structural and magnetic properties of the Co film, through its epitaxial growth on different surfaces, e.g., Ir(001), Cu(001), and Pt(111), one can achieve entirely different in-plane magnon dispersions, characterized by positive and negative group velocities. Our first-principles calculations show that spin-dependent many-body correlation effects in Co films play an important role in the determination of the energies of confined magnon modes. Our results suggest a pathway towards the engineering of the group velocity of confined ultrafast magnons.