Help with soldering contacts on HD-555 Driver

[jschristian44]

So I am fairly new to soldering and don't want to ruin my speaker drivers.  Is it best to use a de-soldering pump or de-soldering wick for something this small.  I have heard wicks are easy.  But to me it seems pumps are easier to just melt what is there and suck it up right away.  But anyways here is the kit I am getting and here is a pic of what I need to de-solder and then re-solder new wires on to.  Any other tips on how to do it would be great as well.  Is too little solder better than too much?  Like I don't want to get any solder on the green part and melt that right?  Thanks!
 
Edit:  Can I just heat up the solder that's already there, pull out the old wires and attach the new ones?
 

 
http://www.amazon.com/Tech-Spray-Desoldering-Wick-Yellow/dp/B000PPV8VU/ref=pd_cp_hi_3
 
http://www.amazon.com/gp/product/B0009Z3JJA/ref=ord_cart_shr?ie=UTF8&m=ATVPDKIKX0DER
 
http://www.amazon.com/gp/product/B0002BBZ2Y/ref=ord_cart_shr?ie=UTF8&m=A3NUNNXXHUJDMF