The Wee Wuns has a sizing and weight guide for BP's (they're good like that). I'm guessing that 44cm is pudgy for a 4 month old? I *think* I remember Riv's waist being in the 30's when he was much older? (He was long and skinny)

Here's how I'd decide:
I'd get a small if: I was going to have more kids anyway, I wanted it now, I didn't think there was a growth spurt on the horizon, I knew that size guides are conservative and nappies often fit a larger range of measurements.
I'd get a medium if: I was happy to wait or use it as a cover til it fit as an AIO, if I wanted to get a lot of wear out of it, bub was growing steadily.

I've just had a thought though - where do you live? We're near Montrose/Croydon area, and I have Medium and Small BP's if you want to have a look and try the covers on your bub!
You can PM me if you don't want to broadcast your suburb.