Since you post here, I assume that you are talking about a solid state amplifier PCB........
10 kHz will only show if something is completly wrong with your layout. Not if oscillation could or will occour when feeding the amp with higher frequencies, and it won't say anything about the behavier for stray capacistance at high frequencies....
If the upper Fo for your amp is 20 kHz it could work, however if your amp has a higher Fo, you have to test it at the Fo limit frequency or even higher.
Also remember that stray capacistance depends on the power going through the tracks, so you should test it under load.
You can check for overshoot and ringing with a much lower frequency square wave. Feed it with a 1Khz square with fast rise and fall times and look for funnly stuff on the leading and trailing edges. Both at the output and at internal nodes.
A square wave, regardless of frequency, will have the same slew, and contain odd harmonics toward infinity until your amp limits the slew rate by filtering out those frequencies above Fo. The 'faster' frequency just allows you to zoom in on the X-axis, so to speak. If 30KHz looks terrible, then the leading edges of the 1KHz also looks terrible, just you can't see it with the larger X-axis scale. Square wave is usually used to test the amp's speed and stability when driving a capacitive load. A pure capacitive load should cause some overshoot, the question is to what degree?
You might post a picture of the waveform(s).
The resistor in the Zobel, series to the cap, may or may not fry but it is a capacitive load and should be removed for the square wave tests.
The lower frequency square wave should be used during checkout because if there is oscillation or cross conduction induced, it will happen less times per second and be less likely to cause a fire. The X axis is easily changed on the scope. If the amp is functioning correctly 30KHz won't do anything other than heat up the zobel at high levels. Remove it? With a resistive load yes, but not with a loudspeaker as the amp may (or may not) become unstable without a resistive high frequency load (which is what the zobel is).
Yes, there are things you won't find. Like those little self-extinguishing bursts of oscillation on the PNP side, right when the NPN physically cuts off - right about -4V peak. Just about any low frequency signal, including music, will find it - if it's at exactly the right level. Square wave can go right through it so a sine is better. These oscillation modes are non-destructive and you can use the amp, and take your time tracking them down. I've never had one due to a PCB parasitic issue, but I've had them with large output stages mounted off-board and with a cascode output stage with no base stoppers (note to self - you CAN'T do that!!!).