The effect of a pair of picosecond pulses on the ionization and deformation of a liquid tin microdroplet is studied for a range of incident pulse parameters. Faraday cups are used to measure ion kinetic energy distributions, together with high-resolution shadowgraphy to monitor target deformation and expansion. It is found that the introduction of a relatively weak first pulse results in an order-of-magnitude reduction of the number of ions with kinetic energies above 1 keV, and a strong shift of the kinetic energy distribution towards lower energies, while the expansion dynamics of the droplet can be kept similar to the single-pulse case. By controlling the relative intensity and the time delay between pairs of pulses with 52 ps duration, regimes are identified in which spherical final target shapes are combined with a reduced high-energy ion yield. The high-energy part of the observed ion distributions has been fitted with a self-similar expansion model, showing a 30-fold decrease in characteristic ion energy for pulse pairs. This combination of results is of particular importance for plasma sources of EUV radiation for nanolithography applications, in which picosecond-laser-produced target shapes can lead to significant improvements in source conversion efficiency, while a low high-energy ion yield is desirable from a source lifetime perspective.