SMPSU noise isn't the major issue, its the leakage current through the class Y capacitor that is commonly fitted from 0V on the secondary side side of the SMPSU to the negative of its primary side DC bus. The capacitor exists to provide a return path for the HF leakage via the interwinding capacitance from the 'hot' end of the primary to the secondary, to let the PSU comply with EMI regulations. Unfortunately, as well as passing HF from the secondary to the primary, it also passes a line frequency leakage current from the primary to the secondary, which although small, has lots of voltage driving it so can easily punch through the gate oxide of unprotected CMOS devices. It is possible to avoid having a capacitor between primary and secondary side, but to do so requires an interwinding screen which pushes up the cost significantly and is usually only found in medical grade PSUs. Its also possible to ground the secondary side to ground out the leakage current, (which is what most modern PCs do), but then there is a small possibility of problems with ground loops when you connect a grounded monitor or printer, and there is still a risk of damage if the PSU ground ever gets disconnected.
Although it would be preferable to use a transformer with two 9V secondaries, as the 9V AC supply goes to a bridge rectifier in the C64, with its negative terminal connected to 0V (chassis ground), you could use a transformer with a *SINGLE* 9V secondary feeding the C64 with 9V AC with a bridge rectifier in the PSU from the same secondary providing the raw DC for the 5V regulator. The negative sides of the two bridges would be in parallel. As you need to avoid overloading the bridge in the C64, use Schottky diodes for the bridge in the PSU, rated for the full secondary current so you can guarantee that its negative side diodes will carry the bulk of, or all the current. If you do this, fuse both AC lines to the C64.
There's no reason *NOT* to use a switching regulator on the secondary side of a conventional mains transformer for the 5V supply - just make sure its output is well filtered. Avoiding a linear regulator is desirable if you want the PSU to run cool.
In all cases I'd fit a TL431 + TRIAC crowbar circuit on the PSU 5V rail to prevent it overvoltaging the nearly irreplaceable C64 if the regulator fails.