Extremely interesting
If I try to find the resonant frequency using oscillator-amp speaker - all of which I have - should I take the strings off ?
I'm leaning to taking them off for this "humming test".
Just thinking that w strings on their tension affects any measurement.
Naturaly all this leads to an endless rabbithole - detuning the guitar higher or lower - as long you play alone.
You may be surprised... string tension doesn't play as much a role in affecting the resonant frequency, as it does determining the shape(s) of the frequencies as the strings are plucked. But that is, indeed, another rabbit hole.
It is not necessary to remove the strings, or to damp the strings, if you are simply humming into the soundhole. You may want to limit your sniffing, especially if people are watching.
If you are applying a tone with a speaker resting lightly on the soundboard (for example), and trying to measure the vibration, you can pick up a whole lot of harmonics if you don't at least damp the strings (usingcloth or a piece of foam, etc).