Synchronous DC-DC converter and fast diodes
After discussing this at university here's the answer: no, it's not possible.

Because if the external diode has a higher V_F value, it will be short-circuited by the low-V_F high-Q_rr internal body diode of the MOSFET. Therefore at turn of the internal body diode will have the same switching losses, since the external diode practically never goes in conduction mode.

The only "solution" seems to be to get a hand of a bit higher (~10-20%) R_DS,on MOSFET which has a better diode (10-20 times lower Q_rr) and eventually put some more MOSFETs in parallel in order to lower conduction losses.