Catalysis of the reaction: [beta-(1->4)-D-glucosamine]n-[N-acetyl-D-glucosamine]m = D-glucosamine + [beta-(1->4)-D-glucosamine](n-1)-[N-acetyl-D-glucosamine]m. This reaction is the hydrolysis of chitosan or chitosan oligosaccharides to remove a D-glucosamine residue from the non-reducing termini; chitosan is a linear polysaccharide composed of randomly distributed beta-(1->4)-linked D-glucosamine and N-acetyl-D-glucosamine units.