Thermoelectric cooler for part cooling fan?
On the printhead?
TECs or Peltier Elements are incredibly inefficient compared to airstream coolers. Their only benefit is perfect temperature control, from which you will have nothing because there is no firmware that cares for the temperature of cooling air or the cooling body of a Hotend. Also, a TEC creates a lot of heat on its output side - which means you heat the air just millimeters away from where you want to cool the air!
To get the heat produced by the TEC away, you either need a rather large cooling body - which is a lot of weight and space you need. As a result, you reduce the maximum print speed a lot. A water cooler isn't necessarily that much lighter, but it also gets us the trouble of having a highly conductive liquid right on the printhead.
lighter alternative: compressed air
You'd have much better efficiency by having compressed air decompress (as in: get out of a slim nozzle) slowly just a few millimeters in front of the air intake of your part cooling fan - expanding air cools down a lot, and running a compressor for a few moments takes less energy than running a Peltier element with the same temperature drop. In a pinch, a CO2 canister could provide the needed high pressure air, and a nozzle like you have it on an airbrush would work.
Move it off the printhead?
As the weight of the necessary secondary equipment is an issue, it might be better to move the Peltier element off the printhead. For example, by using a flexible hose that supplies the air to the cooling fan, and feeding that with precooled air - and now a Peltier element can shine: by having the weight be no longer a matter, we can use a rather large cooling body on the outside and cooling fins on the inside.