New Fan or Peltier

Peltier? No. You'd have more heat to vent than you do now, plus you'd need a separate power supply and a means of dealing with the condensation caused by the Peltier.

Not meaning to be disrespectful, but based on your questions, I doubt that you are capable of modifying a notebook computer. No shame in that, its territory few if any dare to tread unless they have a junk machine they don't care about.

Changing out fans on a notebook is difficult, its unlikely you could find a better fan than what the manufacturer installed. You would have to match the exact size and power specfications.

Installing a Peltier is even more complicated. As mcl noted, the first issue is where you are going to get the power for such. Secondly, I'd doubt if you really understand how a Peltier works. Contrary to popular belief, a Peltier doesn't actually cool (really, very few things other than something that is cold actually cool), it transforms heat energy from a lower temperature on one side to a higher temperature on the other side. That means instead of having say 60C at your CPU you now have 75C a bit over, on the otherside of the Peltier. Yeah, your CPU is cooler, but the heat energy is now maybe 1/4" away and at a higher temperature. So perhaps slightly better heat transfer to the air because its at a higher temperature, but you have even more heat to transfer because of that generated by the Peltier. So your fans will be working even harder. Lastly, have you ever looked inside a typical notebook? There's not much room in there if any at all. So its unlikely you would get it in there.

Your best bet would be to open the machine up (in which case you will get a chance to see how little room is in there) and thoroughly clean the cooling system, possibly even doing the Arctic Silver treatment that's discussed elsewhere in these forums.