Fluorescence line shapes and cooperative spontaneous emission in disordered one-dimensional molecular aggregates are calculated using closed expressions derived by applying the method of optimal fluctuation. A simple scaling relation L-s similar to omega(s)(-1/2) is established between the low temperature disorder-induced Stokes shift omega(s) and the superradiance enhancement factor L-s. Scaling of the Stokes shift with aggregate size, and the time-dependent Stokes shift are discussed as well. Excellent agreement is obtained with numerical simulations.