We investigate the influence of the nucleon-nucleon collision profile (probability of interaction as a function of the nucleon-nucleon impact parameter) in the wounded nucleon model and its extensions on several observables measured in relativistic heavy-ion collisions. We find that the participant eccentricity coefficient, ǫ * , as well as the higher harmonic coefficients, ǫ * n , are reduced by 10-20% for mid-peripheral collisions when the realistic (Gaussian) profile is used, as compared to the case with the commonly-used hard-sphere profile. Similarly, the multiplicity fluctuations, treated as the function of the number of wounded nucleons in one of the colliding nuclei, are reduced by 10-20%. This demonstrates that the Glauber Monte Carlo codes should necessarily use the realistic nucleon-nucleon collision profile in precision studies of these observables. Our study is relevant for hydrodynamic calculations which use the Glauber-model initial conditions. The Gaussian collision profile is built-in in GLISSANDO.