We performed an angle-resolved photoemission spectroscopy study of the Ni-based superconductor SrNi$_2$As$_2$. Electron and hole Fermi surface pockets are observed, but their different shapes and sizes lead to very poor nesting conditions. The experimental electronic band structure of SrNi$_2$As$_2$ is in good agreement with first-principles calculations after a slight renormalization (by a factor 1.1), confirming the picture of Hunds exchange-dominated electronic correlations decreasing with increasing filling of the $3d$ shell in the Fe-, Co- and Ni-based compounds. These findings emphasize the importance of Hunds coupling and $3d$-orbital filling as key tuning parameters of electronic correlations in transition metal pnictides.