From what I have heard, the 97-03 C5 has the tstat and housing as one unit. But the '04 has them separate so you can just replace the tstat itself.....
Possibly replacing the entire unit with an '04 tstat and housing would be a wise move.....
Honestly, I think you could get a cooler running engine in traffic if you just programmed the fans to come on at a lower temp. Just about everyone says you MUST do the fan reprogramming with the 160 tstat anyway, but I think you could just skip the hardware replacement and just go for the programming alone to get the same result.