Reverse recovery time (and possibly sharpness, if it is of a type which has reverse recovery time) is absolutely critical. Think about it: if the diode still conducts for some time when the MOSFET has turned on, the diode and MOSFET form a total short circuit over the low-impedance capacitance you have at the output!
Hence, a schottky type tends to be the only sensible choice; traditional Schottky for low voltages, SiC for high voltages. Schottky diodes have no reverse recovery time (although they do have junction capacitance which causes a similar switching loss element, but this usually isn't a huge problem; by all means calculate it to be pedantic).
Before SiC diodes, we were forced to balance between minimal reverse recovery time and softness factor, and possibly add RC snubbers to dampen the oscillation caused by the short circuit current charging layout parasitic L; or just slow down the MOSFET turn-on time. All such measures caused quite some heavy switching loss. Now with SiC diodes available, with zero reverse recovery time, such practices are usually not needed at all.
Of course, with your 15.5V output voltage, SiC is not needed, a standard schottky (for switching applications!) does better, and such parts have been available for several decades now.
But keep your eye on the reverse leakage spec of the schottky diodes. Lowest Vf types, looking appealing at first sight, may have very high off-time leakage, possibly causing thermal runaway. Likely not a huge problem at Vr=15.5V, unless you run very close to maximum ratings or fail at cooling the devices.
Don't fall into the trap of wondering where the reverse recovery times are listed. Ignore the parameter in parametric searches and don't look for it in the datasheets: it's not listed because schottky diodes do not have this thing at all. (Took me a year to figure this out...)