You don't have to get a full exhaust (unless you want to). But you can't just buy the headers alone......to connect to the stock exhaust you have to make up the empty distance between the header and the stock exhaust, either with off-road connection pipes or hi-flow cats. Whatever LT headers you go with there should be an option or choice for connecting to stock exhaust. How you connect to the stock exhaust depends on how environmentally friendly you want to be
I had Kooks 1 7/8 LT headers with the hi-flow cats when I had my 2011 SS. And to get he most performance out of the setup, had it tuned and dyno tested.
LT Header | off-road pipe | stock catback exhaust
or
LT Header | hi-flow cat | stock catback exhaust