You can use dichlor instead of bleach to shock with but just be aware that most dichlor that is sold these days has unwanted stuff blended into it. Two that we know of that are safe to use are listed on the following page. http://pool9.net/ssr/

If you use trichlor or dichlor, you won't want to add the stabilizer since both of those products have stabilizer (CYA) in them already.