The problem seemed to be down to trying to use, I think it must have been creating an invalid file name:
'%s_%d.dcm'
This code actually works fine, writing to the correct folder, when I simply use:
baseFileName = sprintf('Segmentation_%d.dcm', cnt);
fullFileName = fullfile(pwd, 'Project_Segmentations',baseFileName);
% Write the DICOM segmentation to the folder.
dicomwrite(segmentation, fullFileName);
What I actually want is for the DICOMs to be written with the file name format of 'OrginalFileName_Segmentation.dcm'. If anyone can advise me on this it'd be really helpful, but for now the file name format I'm using is acceptable for my application.