Hi there and welcome to Electronics Point
The general thing you want is a momentary pushbutton. Momentary means that it's spring-loaded and only stays down when there's force on it. Most likely SPST (single pole single throw - means there is one set of contacts) and normally open (means that the contacts are connected when the actuator is pressed down, and unconnected when the actuator is up). So it would be described as an SPST-NO or SPNO (single pole normally open) momentary pushbutton.
There are two basic styles: tactile (aka "tact") and standard. The tact ones make a click when you press them, and release them, and provide tactile feedback to your finger. On non-tactile pushbuttons, the actuator moves smoothly. Your one actually looks like a tact switch. Can you try pushing it directly to see whether it gives you the tactile feedback "feel"? Here's an example of a tact button for reference:
http://www.digikey.com/product-detail/en/B3F-4000/SW411-ND/63961
The footswitch has been designed so that the full force of the user's foot does NOT reach the pushbutton; it's absorbed by the tapered spring. This is essential because these little switches can be damaged by force. So you need to duplicate that arrangement.
Next, you need to match the dimensions. That one looks to be around 12x12 mm so the actuator would be around 6~8 mm. Can you make some measurements and post the results, and tell us whether it's tact or not?
The footswitch part, and the tapered spring, are not included with the pushbutton. You'll have to find them yourself. Or you could just buy a complete footswitch unit, already assembled. Try a music shop - online or locally.