Summarized from my notes on diodes.
So you can readily evaluate the tradeoffs between the diode types:
Schottky Barrier Diode has Qrr < 20 nc.
Regular Schottky has a Qrr ~ 50 nc.
FRED varies with temperature, 30ºC Qrr ~ 150 nC , rising to 450 nC @ 150º. (As bad as ordinary silicon!)
Ultra Fast Recovery Diode varies with voltage, @600 V Qrr ~ 150 nc
Vanilla silicon had Qrr ~ 500 nc.
The Qrr creates a high-frequency carrier which is AM modulated by mains frequency or 2x mains frequency. This signal is broadcast through the amplifier/preamplifier where it is received by any long wire.
The argument is commonly made to use an inexpensive (or least expensive) diode and add a snubber to remove the ringing. This is not the most horrible approach, but the issue is that the snubber must be carefully tailored to rapidly damp the ringing" too little ζ slowly damps the ringing and lets it broadcast noise while too much ζ rapidly damps the ringing but burns power. Remember, the resistor converts the ringing power into heat. So a noisier diode needs a smaller resistor in the snubber which wastes more power.
The manufacturers (such as Cornell-Dubilier) typically provide circuit calculations for SMPS, which is a different can of worms. But using a ζ of 0.5 to 0.707 is generally considered optimal. (The math isn't hard, but there's no easy way to dump my equations in here from Microsoft Word.)
Summary of the issues:
The tradeoff is bigger R, lower ζ, ringing slower damped, noise increases, power consumption is reduced.
The tradeoff is lower R, higher ζ, ringing faster damped, noise decreases, power consumption is increased.
Takeway:
Not adding noise in the first place can be easier than removing it, particularly since diodes with low Qrr are a small expense.