The cell nucleus plays a critical role in mechanosensing and mechanotransduction processes, by adaptive changes of its envelope composition to external biophysical stimuli such as substrate rigidity and tensile forces. Current measurement approaches lack of precise control in stress application on nuclei, thus significantly impairing a complete mechanobiological study of cells. Here, we present a contactless microfluidic approach capable to exert a wide-range of viscoelastic compression forces (10-103 μN) -as an alternative to adhesion-related techniques- to induce cell-specific mechano-structural and biomolecular changes. We succeed in monitoring substantial nuclear modifications in Lamin A/C expression and coverage, diffusion processes of probing molecules, YAP shuttling, chromatin re-organization and cGAS pathway activation. As a result, high compression forces lead to a nuclear reinforcement (e.g. up to +20% in Lamin A/C coverage) or deconstruction (e.g. down to -45% in Lamin A/C coverage with a 30% reduction of chromatin condensation state parameter) up to cell death. We demonstrate how wide-range compression on suspended cells can be used as a tool to investigate nuclear mechanobiology and to define specific nuclear signatures for cell mechanical phenotyping.