The MIDAS (Micro-Imaging Dust Analysis System) atomic force microscope on board the Rosetta comet orbiter investigated and measured the 3D topography of a few hundred nm to tens of mu sized dust particles of 67P/Churyumov-Gerasimenko with resolutions down to a few nanometers, giving insights into the physical processes of our early Solar System. We analyze the shapes of the cometary dust particles collected by MIDAS on the basis of a recently updated particle catalog with the aim to determine which structural properties remained pristine. We develop a set of shape descriptors and metrics such as aspect ratio, elongation, circularity, convexity, and particle surface/volume distribution, which can be used to describe the distribution of particle shapes. Furthermore, we compare the structure of the MIDAS dust particles and the clusters in which the particles were deposited to those found in previous laboratory experiments and by Rosetta/COSIMA. Finally, we combine our findings to calculate a pristineness score for MIDAS particles and determine the most pristine particles and their properties. We find that the morphological properties of all cometary dust particles at the micrometer scale are surprisingly homogeneous despite originating from diverse cometary environments (e.g., different collection targets that are associated with cometary activities/source regions and collection velocities/periods). There is only a weak trend between shape descriptors and particle characteristics like size, collection targets, and cluster morphology. We next find that the types of clusters found by MIDAS show good agreement with those defined by previous laboratory experiments, however, there are some differences to those found by Rosetta/COSIMA. Furthermore, our pristineness score shows that almost half of MIDAS particles suffered severe alteration by impact, which indicates structural modification by impact (e.g., flattening and/or fragmentation) is inevitable despite the very low collection speeds (i.e., ~3-7m/s). Based on our result, we rate 19 out of 1082 MIDAS particles at least moderately pristine, i.e., they are not substantially flattened by impact, not fragmented, and/or not part of a fragmentation cluster.