I have just had my first passenger (RHS) puke on a flight. He started on downwind (after a 1.5 hour flight - couldn't he have done it earlier) and carried on puking all the way into the landing. Very distracting for me as a pilot. Woman in labour - don't even want to contemplate how distracting that would be.
So for me - Mayday and get an ambulance ready please. Maydays are also applicable for serious medical problems, and a woman deep in labour, in a small craft with no qualified help nearby counts as a serious medical in my book. (I'm assuming you're not referring to "I'm feeling a bit of a movement here. I might just have this baby today or maybe early tomorrow." but "My water just broke and I have contractions every three minutes. I can't breathe it off anymore, I'm going to push and I'm having my baby RIGHT NOW.")
Besides, I hope that as far as ATC is concerned, I get the same service as soon as I explained the situation, regardless of whether I declared a mayday or a pan. Unless another craft declares a mayday or pan at the same time. But that is getting to be a very remote possibility now...
But how do you fit one very pregnant lady in a small aircraft? Maybe the RHS of a 172 or 182 would work but all low-wings I know require you to walk over the wing then plonk deep down into a seat somewhere. Even when not in labour, they'll never get out again.