RMS and average value of a DC signal - Which is the correct way to eliminate the inaccuracies due to incorrect measurement setup?
In that case, to properly capture the accurate value of the DC Signal
without the AC Noise ripple, should I use the RMS value of the scope
measurement to capture it or the Mean (average) value of the scope
measurement to capture it?

If you want to know how much power will be flowing in a resistor connected to that DC voltage (plus ripple), then you would use the RMS value displayed by the measurement equipment.
If you want to know the average level of the voltage use the mean level displayed by the measurement equipment.
It all depends on what you want to measure and that depends on why you want to measure it; RMS gives you the effective heating value of the voltage should it be connected to a resistor.
On the other hand, if you were designing an amplifier or a voltage regulator and, you wanted to inspect the &quot;static&quot; errors in the circuit, you'd measure the average level. If you wanted to measure output noise you'd AC couple and measure either the peak-to-peak or the RMS of AC coupled waveform.