Cut the red (middle) wire off your 3-pin JST connector. The two remaining wires (black and white) will connect to either side of your trigger button. You can leave these in a solderless breadboard, or cut the connector's male pins off and solder directly to the button's legs.
I added a long wire extension between my button and my JST connector. This gives me the option to trigger the bark "secretly" from a bit of a distance. Another option would be to place the trigger button on the head or underneath the nose, so he barks when you "boop" him.
Plug your speaker in via the mini jack port on the top of the MonsterM4sk. A small speaker should be able to hide inside Fizzgig's head, or you can add a longer extension cable for more control over where to put the speaker.
Since he's built on a wig, he's perfectly suited to sit on top of something round and head-sized for display. A pumpkin would work perfectly, or a foam wig head works great too. Your speaker can be hidden behind your display. I made a little paw print out of craft foam to put over the trigger button.
I made a wearable version by safety-pinning Fizzgig onto the back of a sheepskin stole. I threaded the button underneath the front of the stole so I can trigger it on unsuspecting followers.