When you have those pieces off and the screws removed, an additional trigger hammer piece will come off the rear, save this also. The barrel seemed stubborn, so I left it glued and just pried the halves up from the rear to work on the interior.
There are many pictures of Han's blaster on the Internet to provide you color choices. Many of them appear to vary the color of the barrel end.
Choose the paint colors you like. Spray paint specifically made for plastic makes a good base. Let the paint dry thoroughly before handling.
You can add weather and wear details.
The amount of "screen accuracy" is always something of an art ranging from simple to expensively complex. A majority of replicas on Etsy and eBay, that are authentically colored, start with the Rubie's toy and add "value" via some paint.
If you want to take "screen accurate" to the Adam Savage extreme, look on http://www.therpf.com/ although such accuracy can escalate the cost and build time significantly.