Fingerprinting-based positioning significantly improves the indoor localization performance in non-line-of-sight-dominated areas. However, its deployment and maintenance is cost-intensive as it needs ground-truth reference systems for both the initial training and the adaption to environmental changes. In contrast, channel charting (CC) works without explicit reference information and only requires the spatial correlations of channel state information (CSI). While CC has shown promising results in modelling the geometry of the radio environment, a deeper insight into CC for localization using multi-anchor large-bandwidth measurements is still pending. We contribute a novel distance metric for time-synchronized single-input/single-output CSIs that approaches a linear correlation to the Euclidean distance. This allows to learn the environment's global geometry without annotations. To efficiently optimize the global channel chart we approximate the metric with a Siamese neural network. This enables full CC-assisted fingerprinting and positioning only using a linear transformation from the chart to the real-world coordinates. We compare our approach to the state-of-the-art of CC on two different real-world data sets recorded with a 5G and UWB radio setup. Our approach outperforms others with localization accuracies of 0.69m for the UWB and 1.4m for the 5G setup. We show that CC-assisted fingerprinting enables highly accurate localization and reduces (or eliminates) the need for annotated training data.