Do you think if I disconnect the fan and put and external fan on the side of the PC will do the necessary for cooling it?
I wouldn't recommend that course of action, pulling the plug of your GPU's cooling fan is like spelling out death for the processor. If a simple side mounting computer case fan would do the trick, than most video card companies wouldn't waste the bucks on producing cooling solutions for their cards, they would just run with the computer case cooling solution option. That small fan is on top of that GPU for a reason, I wouldn't mess around with it!