You can do it with a linear supply, a common mod that people do is actually to replace the lm7805 regulator with a pin compatible switching replacement for less power draw and heat generation.
The PSU also supplies 9V AC (this is not a mistake). The C64 is quite sensitive to over-voltage, so your switching supply might work, or it might kill it because there are voltage spikes which modern equipment doesn't care about, but the C64 will.
The PSU situation isn't great: building your own is difficult (see https://www.c64-wiki.com/wiki/Power_Supply), and using an old "real" PSU is risky, because they tend to produce >5V as they die, taking the C64 with them. That's why I ended up using the Ultimate 64 rather than a real C64: just supply it with 12V DC from basically anything, and it will be fine.
Why would you blow it up with a SMPS? I built a PSU for mine with a 5V switch-mode wall wart that originally powered a USB hub and it works fine. There's a 100uf filter cap on the 5V rail inside the machine already that will smooth things out. The real danger is letting the 5V rail get too much over voltage; that's what happens with the original power supplies, and it will cook the RAM chips in a hurry.
I thought I'd try to turn it on but got spooked by the requirements for the PSU
I understand it needs ripple free 5VDC 2-4A+ through a 7 pin din
Am I really going to blow the unit up with a switch mode, does it really need linear regulation?
What's stopping me using 2-3 LM7805s in parallel?
[Background] former burnout frontend dev working at an electronics shop