I said this in another thread, but there is actually a book about Khajiit monks in Morrowind, here's the book: http://www.imperial-library.info/content/morrowind-master-zoarayms-tale
Spoiler The dumner man who beats Master Zoaraym, Taren Omathan, can be found in game as the master trainer in handtohand, too.
So a Khajiit monk might be cool, just some food for thought concerning your character.