Unless it's a too-small module intended to be placed within a system that's ultimately filtered -- it contains a filter (and CMC) already.
Consider the PSU as a three-terminal device. The two mains leads are one, the two output leads are another, and the chassis ground (or ground screws for the loose PCB kind) is the third.
If ground isn't present, or connected*, then the two leads (mains and output) are a through circuit, and a choke can be put on either one, equivalently. It's better to put it on the mains side, because the wire can be smaller = more turns on a given core.
*Even if you don't physically connect it, notice there is still a stray capacitance to the surroundings.
If it is connected, then there's probably some "Y" capacitance to it which improves filtering, and the noise level can be different on both ports. In that case, extra choking impedance in series, or bypass capacitance in parallel (to ground), will help, and you have a choice of which port to quiet down more.
If you can't demonstrate you need it, though... what's the point in adding it at all? Just a "feel good" act? But it's just superstitious then. That doesn't make me feel good, at least...
You don't need expensive instruments to demonstrate some sort of effect. Is the amplifier susceptible to RF rectification? Is anything nearby or attached, susceptible? Mind, while this gives a testable hypothesis, it is only a tiny step above guessing in the dark. While technically possible to reason your way out, it requires an unnatural amount of observation and discipline to succeed. You may find it helpful to use a radio (an AM or shortwave radio would be best) to get some idea of efficacy.
Tim