Kartboy spacers won't work with all speakers, make sure you're pointing him towards ones that fit. Since we don't know exactly what model speakers he has, I wouldn't be so assumptive
Also, don't tape the wires, that's messy and unreliable. If you're new to this game, then soldering isn't gonna happen, just invest in some decent butt connectors or crimp caps (a good set of crimpers is key as well, those cheapos are crap) and tie in the new wires.
Do you know how to test the polarity to make sure the speakers are wired up correctly? If they aren't, you'll have crappy sound, zero bass, and your ears will be angry.