We illustrate the computational advantages of the recently introduced single-boson exchange (SBE) formulation for the one-loop functional renormalization group (fRG) applied to the two-dimensional Hubbard model. We present a detailed analysis of the screened interactions and Yukawa couplings and their evolution with temperature and interaction strength, both at half filling and finite doping. We find that the rest functions describing the corrections beyond the SBE contributions play a negligible role in the weak coupling regime, except for the vicinity of a pseudo-critical transition. However, even in this situation the impact on the resulting self-energy and physical susceptibilities is of marginal importance. The SBE formulation of the one-loop flow hence allows for a substantial reduction of the numerical effort in the treatment of the two-particle vertex function, paving a promising route for future multiboson and multiloop extensions.