Context. Recent evolutionary computations predict that a few percent of massive O-or early-B stars in binary systems should have a dormant BH as a companion. However, despite several reported candidate X-ray quiet OB+BH systems over the last couple of years, finding them with certainty remains challenging. Yet these have great importance as they as they can be gravitational wave (GW) source progenitors, and are landmark systems in constraining supernova kick physics. Aims. This work aims to characterise the hidden companions to the single-lined spectroscopic binaries (SB1s) identified in the B star population of the young open Galactic cluster NGC 6231 to find candidate systems for harbouring compact object companions. Methods. With the orbital solutions for each SB1 constrained in a previous study, 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 spectral signature of a stellar companion, we performed atmospheric and evolutionary modelling on the primary (visible) star to obtain constraints on the mass and nature of the unseen companion. Results. For 7 of the 15 apparent SB1 systems, we extracted the spectral signature of a faint companion, resulting in seven newly classified SB2 systems with mass ratios down to near 0.1. From the remaining targets, for which no faint companion could be extracted from the spectra, four are found to have companion masses that lie in the predicted mass ranges of neutron stars (NSes) and BHes. Two of these targets have companion masses between 1 and 3.5 M , making them potential hosts of NSes (or lower mass main sequence stars). The other two have mass ranges between 2.5 to 8 M and 1.6 and 26 M , respectively, and so are identified as candidates for harbouring BH companions. Conclusions. We present four SB1 systems in NGC 6231 that are candidates for harbouring compact objects. However, unambiguous identification of these systems as X-ray quiet compact object harbouring binaries will only result from photometric and interferometric follow-up observations of these objects.