Well, first, it could be that your mis-adjusted waveshape control is what's giving that nice sound, so it's up to you whether you feel you need to tweak it any further. If it ain't broke...
I don't know what kind of scope you're using, and I'm not experienced with anything but my cheapo digital scope. But you don't need to send a signal at all into the circuit. What you're looking at when tweaking the waveform is the LFO, which is a free-running oscillator that's going all the time, even without any signal input to the circuit. You might need to set your scope for DC coupling to see the LFO properly.
Yes, you should be able to see it even with the optional cap installed. You can see the signal at the center lug of the Depth knob as well. So that's the LFO, and that's what should look like a triangle in one of the switch positions (which one is triangle actually depends on which way you read the wiring diagram when you wired it - you can look at the switch as if it's drawn from the bottom or the top - both will work the same, just with different positions for the different waveforms).
It should look like a square wave, a ramp wave going up, a ramp wave going down, and then the last wave that isn't one of these three is supposed to look like a triangle, but it probably won't when you first look at it.
