Yes, it may be easiest to think of wanawake as simply an irregular plural (and thankfully, there are very few irregular anythings in Swahili!).
But the deeper grammatical answer is that mwanamke is actually a contraction of two words: mwana + mke (denoting female). When it changes to plural, both halves change from m- to wa-. (Note: in the case of mwana, a "w" is inserted after the m- prefix because it is followed by a vowel. And yes, you are right about what the regular plural would be.)
How does one say in Swahili, "Go home Emilian. You're DRUNK!" I ask because I'm fairly certain this is not a Kenyan woman, nor a woman of any kind. Further, I'm also certain this is the same man who, in earlier lessons identified himself as 'Emilian'. Emilian si mwanamke. Emilian ni mwanaume, na ninafikiri amekuwa akinywa.