Neither of the solutions is correct, I think that the arrangement misled you.

I've rearranged the capacitors. Does it help in calculating the total capacitance?

The trick is, figure out how the current flows from A to B, where it branches and where it merges again.

Case 1

^{simulate this circuit – Schematic created using CircuitLab}

Case 2

^{simulate this circuit}

That'll work.

Assuming you want 'reasonable' values, choose R1 somewhere between 1k and 100 kohm. Choose C so that 0.7*R1*C is the time you need. Choose R2 << R1, but at least 10 ohm (to protect the switch from arcing when you use it to discharge the capacitor.

So to charge in 10 seconds (consider that a long time), choose R1 = 100k. Then C is (10/70k) = 150 uF.

Note that capacitors are not particularly accurate (neither is the schmitt trigger), so your results may vary. It's easier to modify R1 to adjust.