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Recent evolutionary computations predict that a few percent of massive OB stars in binary systems should have a dormant BH companion. Despite several reported X-ray quiet OB+BH systems over the last couple of years, finding them with certainty remains challenging. These have great importance as they can be gravitational wave (GW) source progenitors, and are landmark systems in constraining supernova kick physics. This work aims to characterise the hidden companions to the single-lined spectroscopic binaries (SB1s) in the B star population of the young open Galactic cluster NGC 6231 to find candidate systems for harbouring compact object companions. With the orbital solutions for each SB1 previously constrained, we applied Fourier spectral disentangling to multi-epoch optical VLT/FLAMES spectra of each target to extract a potential signature of a faint companion, and to identify newly disentangled double-lined spectroscopic binaries (SB2s). For targets where the disentangling does not reveal any signature of a stellar companion, we performed atmospheric and evolutionary modelling on the primary to obtain constraints on the unseen companion. Seven newly classified SB2 systems with mass ratios down to near 0.1 were identified. From the remaining targets, for which no faint companion could be extracted from the spectra, four are found to have companion masses in the predicted mass ranges of neutron stars (NSes) and BHes. Two of these have companion masses between 1 and 3.5 $M_{\odot}$, making them potential hosts of NSes (or lower mass main sequence stars). The other two are between 2.5 to 8 $M_{\odot}$ and 1.6 and 26 $M_{\odot}$, respectively, and so are identified as candidates for harbouring BH companions. However, unambiguous identification of these systems as X-ray quiet compact object harbouring binaries requires follow up observations.