Low power switch input with MCU wake-from-sleep interrupt?
Why are you using falling edge for interrupt at all? However small, you still have some current permanently flowing through the pull-up, which defeats the purpose of sleep mode. Plus the pull-up makes you RC filter lopsided.

Anyway, you have several options. First, you can use SPDT switch which will guarantee same timing for charge and discharge. See first schematics below (BTW, it works for either edge).

If you want to keep using rising edge and SPST switch you can


use two identical resistors, but shunt one of them with diode, resulting in almost the same rising and falling times (tweak one of the resistors to counter voltage drop on a diode, if you wish), and   
recalculate your RC for high resistance and much smaller capacitance, to keep quiescent current low for the same time constant, e.g. 50k resistors and 0.1 &micro;F capacitor.