stoping clicks from audio button

I have a simple circuit that I have that outputs a squarewave to a mono audio jack. I hook this up to an amplifier (like a guitar or keyboard amp) with a standard 1/4" guitar cable. And I have a normally-open switch at my output that when I hit it, it connects my squareqwave output to the guitar amp. So, basically I hit the button I hear a tone.

My goal is to use this along with a slider or potentiometer to play different tones out of the amplifier, by moving the pot and hitting the button... and everything works fine, except everytime I hit the button I hear pretty loud clicks and pops from what I'm assuming is just the noise of the physical metal contacts of the switch hitting together...

Does anyone know a way to rememdy the initial contact noise I'm hearing? I'd like to be able to press the button as fast as I can and only hear the squarewave tone and no clicks.

much thanks!

What is the amplitude of the squarewave? Is it centered about zero volts or is it single-sided such as 0 to +1V. If single-sided you may be hearing the pop from the DC offset of the signal (audio needs to be centered plus and minus around ground). To do this run the signal through a capacitor and resistor to ground (say 0.1µF and 50kΩ).

I'm actually doing a sine and a squarevwave, there's a volume knob that goes from 0 to about 2 or 3 volts in amplitude, I have blocked the DC before going to my output, my output is centered around zero.

Is the switch before or after the capacitor?

Here's a quick sketch of what I've got goin on, the capacitor is before the switch.

Try adding a resistor to ground between the C3 output and switch, about 100kΩ or so, and see if that helps.