The probably best and easest would be the 16S RNA amplification with cyanobacterial specific primers and comparison with genebank (but be sure that the culture is axenic);
Classification based on morphology just help you to identify only genus (in some cases, by very special morphology, even species), but nowadays some of the taxons (genera or species) are undergoing novel classification at genetic level (so already some species would not correspond to the classification in above mentioned books)...
According to WHO (1999, Chapter 12, ISBN 0-419-23930-8 it is preferable to give only the genus name, especially if differentiation between species by microscopy is uncertain on the basis of current general taxonomic knowledge, a lack of locally available expertise, or lack of characteristic features of the specimens to be identified. This must be emphasized because "good identification practice" has frequently been misunderstood to require determination down to the species level, and this has lead to numerous published misidentifications of species.
I think that Komárek and Anagnostidis (1986) and Anagnostidis and Komárek (1988) are very good instruments to help us in the determination of Cyanobacteria genera and species.
It really depends on the cyanobacteria considered. Some are quite easy to identify to the species levels based on morphological characteristics. Some aren't. Indeed, you sometimes need to be able to observe the morphology of heterocyst and akinetes which may not be present (it depends on the environmental conditions experienced by the cyano at the time of sampling).
I am not convinced that the 16S by itself allow identifying cyanos at the species level. I would say its ok at the genus level at best. I do think multi-locci approaches are necessary for "species" characterisation. The best being to use a polyphasic approach (including genotypic, chemotaxonomic and phenotypic characteristics). When speaking about cyanobacteria species, one has to bear in mind that they are bacteria and that the concept of species in the bacterial kingdom isn't clear...