Yes you can. Replacement shell can be ordered online from alibaba or ebay. And easy to follow tutorials are available on Youtube. Link for best one is here https://www.youtube.com/watch?v=6O6R59ey... I have done it 4-6 times successfully and its very easy. You would require two screwdrivers tri-wing (having three ends) & four end one. Please let me know if you require any additional information.
Even i faced same issue. One by one all buttons stopped working. Issue is with the conductive film circuit; which wears out and stops working. You need to first open your DS4 and note the model number of Motherboard circuit, based on which you can buy the conductive film from Ali Express or Amazon. Cost of the film is about $2-$4. You can replace it on your own. Please contact me if you have any query. @tumharajai (InstaGram) DualShock 4 Button Flex Board Replacement