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In the past decade, HCI surveys provided new insights about the frequency and properties of substellar companions at separation larger than 5 au. In this context, our study aims to detect and characterise potential exoplanets and brown dwarfs within debris disks, by considering the SHARDDS survey, which gathers 55 Main Sequence stars with known bright debris disk. We rely on the AutoRSM framework to perform an in-depth analysis of the targets, via the computation of detection maps and contrast curves. A clustering approach is used to divide the set of targets in multiple subsets, in order to reduce the computation time by estimating a single optimal parametrisation for each considered subset. The use of Auto-RSM allows to reach high contrast at short separations, with a median contrast of 10-5 at 300 mas, for a completeness level of 95%. Detection maps generated with different approaches are used along with contrast curves, to identify potential planetary companions. A new planetary characterisation algorithm, based on the RSM framework, is developed and tested successfully, showing a higher astrometric and photometric precision for faint sources compared to standard approaches. Apart from the already known companion of HD206893 and two point-like sources around HD114082 which are most likely background stars, we did not detect any new companion around other stars. A correlation study between achievable contrasts and parameters characterising HCI sequences highlights the importance of the strehl, wind speed and wind driven halo to define the quality of high contrast images. Finally, planet detection and occurrence frequency maps are generated and show, for the SHARDDS survey, a high detection rate between 10 and 100 au for substellar companions with mass >10MJ.