Okay, so I'll contradict myself: I've identified the chip as a Texas Instruments TPS63060DSC. The data sheet gives the typical quiescent as 30uA (60uA max) with 5V input and 0mA output, which is consistent with the Pololu claim of <0.1mA. So in your position, I'd work with a value of 100uA input current when driving 10uA output, but get one and test it to be sure. Don't even think of using the shutdown feature, since the input pin has a 100k pullup and pulling it low will take 45uA with 4.5V battery voltage. Hope that helps.