If the negative terminal of the SMPS is tied to mains earth inside the SMPS brick then you will probably also have the problem that the negative output terminal of your linear regulator will not be at mains earth potential, but rather several tens or even hundreds of millivolts above it. This is just plain Ohm's law, if the negative conductor of the output cable from ths SMPS brick has tens of milliohms of resistance, and if there is an amp flowing through it, then both ends won't be at the same potential, and if the end at the SMPS brick is at mains earth then the other end isn't. This could cause problems in any sensitive measurements that you make with an oscilloscope, as your circuit's ground will differ from that of the oscilloscope even with the ground clip in place. It's the same reason why you hear CPU-related buzzing noises when plugging the audio output of a laptop into the single-ended line inputs of a grounded domestic hifi amplifier.
That particular problem can be avoided if you choose a class II SMPS power brick that does not need any mains earth connection for electrical safety. In this case you get a different problem in that they usually connect a ~2nF capacitor from the mains wiring to the output wiring, so that your output will have potentially a hundred or more volts of mains voltage on it, if not grounded. There can be very large instantaneous currents if you make a connection from the circuit you are testing to some other grounded circuit at an inopportune time. For example when connecting the audio cable between a grounded hifi amplifier and a class II CD player, if the signal pin of the cable touches first, a spike of current due to the ~2nF capacitor being charged to a couple of hundred volts could damage the input devices of the hifi amplifier. Although the capacitor has a high impedance at 50/60Hz, it does not have a high impedance at the much higher frequencies present in a sudden step such as caused when making a connection.
As long as you are aware of the above limitations, a SMPS power brick might be a sensible thing to use.
There should be much less capacitance from the mains to the output if you use a mains transformer. In the olden days you could buy mains transformers with an earthed screen between the mains windings and the secondary windings, which reduced capacitive coupling from the mains. For test instruments, they used to make transformers with two or even three separate screens between the primary and secondary. E.g. the mains winding would have its screen connected to mains earth, the secondary winding would have its screen connected to the 0V terminal of the secondary winding, and there would be no capacitive leakage currents to disturb the circuit under test. I wonder how people do this these days - can you still get such transformers?