The 1N4937 is OK. The switcher should not be that extremely fast.
With the first two caps one might in theory get away with 50 V ratings, but 100 V or more is definitely better. One should not use a tantalum cap close to the maximum rating and no way well beyound that. They caps may be a littel smaller for a first test, if the 1 M resistor is increased to reduce the pulse rate.