The cross-section of a collision is a direct result of the underlying interactions between the colliding particles. In the low collision energy regime, it can have strong variations as a function of the energy, due to quantum effects. We report on a method for controlling cold atom-ion collision energy by shuttling an ultra-cold Rb atom cloud towards a trapped Sr+ ion. This is done by sweeping a vertically, one-dimensional optical lattice with cold Rb atoms, on an ion in its motional ground-state. This technique permits a delicate control over the collision energy between the ion and a single atom, where its resolution is limited only by the ion temperature. This resolution is one order-of-magnitude better than in previous experiments measuring cold atom-ion collisional cross-section energy dependence. We demonstrate this method in a proof-of-concept chemistry experiment by measuring the energy dependence of the inelastic collision cross-section of an Sr ion in a metastable excited state decaying into its ground state after colliding with an Rb atom in its ground state. This known as a non-adiabatic Electronic-Excitation-Exchange (EEE). We found that for collision energies ranging between 0.2-12 kB•mK, the EEE cross-section obeys the classical Langevin cross-section. This method can be extended for measuring various inelastic processes cross-sections and its high energy resolution enables detection of deviations from the classical cross-section.