From what I know of Tamrielic lore, there are three known assassins' organizations: The Morag Tong, the Dark Brotherhood, and the Shadowscales (now a subsidiary of the DB). The Morag Tong is a Mephala-worshipping Dunmer-centric organization, the DB seems (even though it was, according to some sources, founded by a Dark Elf) a more human-centric organization, while the Shadowscales are purely Argonian.

From an Altmeri perspective, joining any of the two known available guilds (MT or DB) would require a massive amount of pride to be swallowed, even for a psychotic, murderous High Elf. One of them is more or less exclusively run by Dunmer, and one of them worship a Dunmer as their spiritual leader and guide. My question is this: Is there anything in lore (I haven't read the more obscure texts yet) indicating that the Altmer have their own guild of assassins?

From what we know of the Altmer, intrigue and in-fighting would lead us to believe that the demand for assassins would exist on Summerset Isle - I just can't imagine them calling on the services of the MT or DB, for the same reasons I mentioned earlier.