The molecular dynamics study of fragmentation in peripheral $^{197}$Au +$^{197}$Au collisions at 35 MeV/nucleon is presented to probe the nuclear matter compressibility in low density regime. The yields of different fragment species, rapidity spectra, and multiplicities of charged particles with charge $3\leq Z \leq 80$ are analyzed at different peripheral geometries employing a soft and a hard equations of state. Fragment productions is found to be quite insensitive towards the choice of nucleon-nucleon cross sections allowing us to constrain nuclear matter compressibility. Comparison of calculated charged particle multiplicities with the experimental data indicates preference for the \emph{soft} nature of nuclear matter.