wow, for a beginner I would say that the oscilloscope is the best choice
cheers !
No he did say that "it will not hurt" - i.e. will be useful. That's not quite the same thing. And I agree with that - checking noise levels at the output of the PSU without a scope is difficult, not everything can be heard!
You can have e.g. 100kHz noise from one such switching supply superimposed on the power rail, another such supply for another gizmo will produce 115kHz and these get parasitically mixed together somewhere in an amplifier or the console - producing a nasty 15kHz squeal that will be very hard to debug. If you are unlucky, the superimposed noise could get amplified and blow out your tweeters as well, depending on the setup.
So don't assume that when the output is silent there is no noise there - you can easily have high frequency noise or even oscillations there that you can't hear. And without a scope you will never know.
I also concur with the idea that buying a $2 supply and then trying to improve it by adding filters and what not is a fool's errand. Even if that $2 supply isn't explicitly a deathtrap (most of these are - that's why the link to BigClive's videos - he is an electrician and shows what to look for when checking such gadgets for basic safety), just the components needed for the filter will cost you at least 10x as much. Plus work, time and the risk that something blows up catching fire or electrocuting someone because you are dealing with mains. Is that worth saving the 30-40 bucks you would pay for a proper and safe wallwart? You could probably even get a free one if you scavenge one from an old laptop, printer or a similar device - they are still switching supplies but likely of much better quality.
Re your pedal - the most logical thing to do would be to shield the coil in the pedal (build a metal can around it) instead of trying to shield everything else around. What if your colleague puts his big guitar combo (or whatever) next to your pedal and you start picking up noise from his power supply/amplifier? If you can't shield it, you can try to replace the inductor(s) with toroidal ones, those are "self-shielding" because the magnetic field is confined inside the core.