As this project will be used independently of the lab once it's finished I do in fact need to make a dedicated power source.
That is problematic, and no, you ordinarily would not use a switching power supply for an audio application, unless you *really* know what you are doing in quiet switcher design.
The problem is that you need to take AC Mains power in (120Vrms in the US), and step that down to lower voltages (or split voltages in your case). The step-down stage is also used as a safety barrier normally, to give you electrical isolation between the wall power and your output power. You need to follow good design and construction practices when dealing with AC Mains input connections. There are very important rules for how you wire the input switch, fuse and ground connections, and how you make connections to your main input transformer. I've built a few home projects that use AC Mains input power, but I was *super* careful to follow the UL design rules and make my devices safe, even though I never submitted these personal projects to UL. I have also designed products in my EE work that have been qualified by UL for sale. It's not something that you can be taught in a web forum -- you'll need to get a good book at the very least to help you in starting to build audio projetcs like this that use AC Mains power input.
And then you have the added problem that your output voltages exceed the 42Vdc max (or I think 60Vdc max in Europe) that is consided SELV (safe extra low voltage), or safe for people to touch. Voltages higher than that need to use connections and encloures that prevent contact with humans, especially human fingers. There is actually a UL test finger that they use...LOL. There are some technologies that are older than this UL SELV rule, like the -48Vdc of POTS (plain old telephone sets) and phone lines, and those may be grandfathered by UL. But I honestly don't know how high power stereo-to-speaker connections are handled, if they involve enough power to exceed SELV. Hopefully again the good audio project design book will give you good info on this.
I'll google a bit to see if I can find a good starter hobby audio construction book...
EDIT -- Yeah, books like these... I googled +stereo +power +electronics +project +design +book, and got to some good books on Amazon:
https://www.amazon.com/gp/product/0071341196/?tag=pfamazon01-20