Storing and accessing information in atomic-scale magnets requires magnetic imaging techniques with single-atom resolution. Here, we show simultaneous detection of the spin-polarization and exchange force, with or without the flow of current, with a new method, which combines scanning tunneling microscopy and non-contact atomic force microscopy. To demonstrate the application of this new method, we characterize the prototypical nano-skyrmion lattice formed on a monolayer of Fe/Ir(111). We resolve the square magnetic lattice by employing magnetic exchange force microscopy, demonstrating its applicability to non-collinear magnetic structures, for the first time. Utilizing distance-dependent force and current spectroscopy, we quantify the exchange forces in comparison to the spin-polarization. For strongly spin-polarized tips, we distinguish different signs of the exchange force which we suggest arises from a change in exchange mechanisms between the probe and a skyrmion. This new approach may enable both non-perturbative readout combined with writing by current-driven reversal of atomic-scale magnets.