If you are using a commercial controller you will not need the blocking diodes as there is usually a disconnecting MOSFET switch within the controller.
The purpose of a blocking diode is avoid a backwash of leakage current through panel from battery when there is little or no generation from panel. There is a second application where bypass diodes are placed on a panels or every 3 to 6 cells to bypass them when they are shaded. This only works if you have high enough voltage stack and an MPPT controller where there is enough overhead voltage to afford the drop out of a panel that is shaded. You actually don't need an MPPT controller but having an excessive voltage stack would be wasteful for a simple ON-OFF PWM controller.
Cells act like an illumination based current source that is clamped by inherent diode of cell. No load voltage, Voc, is where all the illumination current goes down the inherent diode of the cell. Normal MPP voltage is just below where the inherent cell diode starts to conduct significant current. Typically about 3% of illumination current is allowed to leak down the inherent diode so you get the highest possible voltage on the cell. At 25 deg C this is about 0.53 volts D.C. but, as a normal silicon diode, it has a negative temperature coefficient and the MPP voltage goes down at higher temperature. In the sun, in summertime, depending on ambient temp, the cells may get to 60 deg C and the MPP voltage will drop to about 0.42 vdc per cell.
The reverse leakage on a PV cell in the dark depends on quality of cell and its temperature. Good quality monocrystaline cell has very low reverse leakage (assuming you stay well below the stackup sum of the inherent diode forward bias voltage).
A schottky diode has a low reverse breakdown voltage, as you said 40 volts PIV. If the battery side to cell side exceeds this voltage the schottky diode will zener out.
The larger the diode area, the lower the forward current density and therefore the lower the diode forward voltage drop. If you use a silicon diode with higher current rating it will generally have less forward drop. Keep in mind that the forward voltage drop times the current through the diode will be the heat dissipation in the diode. A larger diode area (higher current rating) will have more junction capacitance but this is of little importance in this application.