Axle

The Blaster in your pic is an 88-02. You can't put a Banshee axle in that without spending some money on a hydraulic brake upgrade. Do not listen to what some people say about shimming things by stacking washers.
 
Yes you would have to do a carrier swap to 03+ to have rear brakes. I've heard the tusk axles are nice.
It would probably cost less to do a banshee axle swap. but be sure you find a rear carrier set up and brakes before ordering so you can get a grand total.
Keep in mind to upgrade to 03+ brakes you would have to weld mounts on the frame to hold the master cylinder and other components.

Tusk, durablue and G-Force axles are the most common aftermarket axle. prices differ, and even different types
Tusk adjustments $200 -
  • Adjustablity Blaster - 4 5/8" to 6 5/8" Total width over stock
Durablue $380
  • The Durablue 2+2 Eliminator axle gives you a choice of increasing the rear axle 2" or 4" wider than the stock axle.
G-force- i cant find this one on rocky. but i think it was about the same as durablue

those are sale prices on rocky right now. $200 for that tusk is a pretty good deal
https://www.rockymountainatvmc.com/p/733/32078/Tusk-Adjustable-Width-Racing-Axle?v=238