We analyse velocity fluctuations in the solar wind at magneto-fluid scales in two data sets, extracted from Wind data in the period 2005-2015, that are characterized by strong or weak expansion. Expansion affects measurements of anisotropy because it breaks axisymmetry around the mean magnetic field. Indeed, the small-scale three-dimensional local anisotropy of magnetic fluctuations (deltaB) as measured by structure functions (SF_B) is consistent with tube-like structures for strong expansion. When passing to weak expansion, structures become ribbon-like because of the flattening of SF_B along one of the two perpendicular directions. The power-law index that is consistent with a spectral slope -5/3 for strong expansion now becomes closer to -3/2. This index is also characteristic of velocity fluctuations in the solar wind. We study velocity fluctuations (deltaV) to understand if the anisotropy of their structure functions (SF_V) also changes with the strength of expansion and if the difference with the magnetic spectral index is washed out once anisotropy is accounted for. We find that SF_V is generally flatter than SF_B. When expansion passes from strong to weak, a further flattening of the perpendicular SF_V occurs and the small-scale anisotropy switches from tube-like to ribbon-like structures. These two types of anisotropy, common to SF_V and SF_B, are associated with distinct large-scale variance anisotropies of deltaB in the strong- and weak-expansion data sets. We conclude that SF_V show anisotropic three-dimensional scaling similar to SF_B, with however systematic flatter scalings, reflecting the difference between global spectral slopes.