Let me start off by saying this might seem like it is to much but once you get into it you will see it isn't really as much as it seems.
The shock on a STT is the same height as the R, the difference is in the length of the reservoir line, I will attach a pic of the Ss shock next to an R shock, either will work but some mods might need to be done to fit the STT reservoir since it is so short.
Also the longer swing arm mounts the bottom of the shock further back so it will lower the bike drastically ~3 1/2", I will also attach a picture of a bracket I had made to fix the problem. Also you will need to either lower the front by slipping the forks or get Scg forks, if you don't build a bracket to accommodate the proper height. If you do lower it you will also need to shorten the kick stand to accommodate.
To the oil lines, they are completely different, so both of you will need custom lines to make the swap work. I used the front hard lines and had braided line made to length to fit to the swing arm.
Thing you dont need to worry about are the swing arm will bolt right up, the wheel will mount, the brake line is long enough, the sprockets wont be an issue since you have an '05 ('03 had a different sprocket).
Shock difference, the STT just has a different color spring.
Bracket, if you draw a straight line through the shock the bottom needs to be mounted lower than the swing arm mount to keep it from flipping backward. Note too I wanted my bike to be lowered so my bracket is actually setup to give the bike a 2" drop, if you wanted to maintain the stock height you would need a different height bracket.
Oil lines stock hard lines then custom to the rear.
Here are how the lines are run
Then a couple shots of my bike. The good stuff!! I also have a S tail swap and chopped the fairing down a few inches.