The effect of solvent selectivity on the chain exchange kinetics for two polystyrene-b-poly(ethylene-alt-propylene) block copolymer micelles (SEP 26-70 and SEP 42-64, where the numbers denote the molecular weight of each block in kg/mol) was investigated in pure squalane and in binary mixed solvents of squalane and 1-phenyldodecane, using time-resolved small-angle neutron scattering (TR-SANS). The exchange rate accelerates by 5 orders of magnitude for both micelles when adding only 25 vol % 1-phenyldodecane to squalane, compared to micelles in pure squalane. This acceleration is attributed to two factors: faster relaxation dynamics of the core blocks as more solvent penetrates into the core, serving as a plasticizer, combined with a reduced energy barrier for chain expulsion due to the lower Flory-Huggins interaction parameter χ between the core block and the solvent. By fitting the TR-SANS data to an established theoretical model, the enthalpic penalty of chain expulsion is determined for SEP micelles in mixed solvents. These results are quantified by a χ-dependent function derived from Flory-Huggins theory, where χ values between the polystyrene (PS) core block and binary mixed solvents are estimated by a combination of static light scattering and cloud point measurements with PS homopolymers. This work quantifies the role of χ in chain exchange kinetics of block copolymer micelles.