The chemical potentials of spherical and diatomic dumbbell particles dissolved in a hard dumbbell fluid are determined using the Widom insertion Monte Carlo simulation method. Results obtained as a function of fluid density and solute-solvent size ratio are compared with previous simulation results and analytical hard body fluid expressions derived from bonded hard sphere (BHS), scaled particle theory (SPT), and corresponding hard sphere (CHS) equations of state. The BHS predictions best represent all the simulation results, while SPT predictions are comparably accurate except for small solute particles dissolved in high-density fluids, and CHS predictions are exact to first order in solute size and solvent density but somewhat less accurate for large particles at high densities. Simulations of the excess reaction free energy for model dissociation and isomerization processes illustrate the subtle effects of solute shape on cavity formation energy for particles with identical molecular volumes.