Billy, I don't know much about the C5s, as a matter-of-fact, I wasn't aware that the newer C5s still had the skip-shift feature (C.A.G.S.); I knew it was there beginning with the ZF Six-speed, but didn't know they still had it.
Anyhow, I found this for you -- CAGS Eliminator Installation -- maybe it can help you, but I can't find a whole lot more specific to your year Corvette. Sorry.
CAGS, for computer-aided gear selection, is a system that forces a first to fourth shift at light loads and low speeds. Most people think this is done for gas mileage but it exist just as much to help the Corvette get through the pass-by noise test as it is to improve fuel economy. CAGS, or "skip shift" as engineers call it, as been a feature on all manuals since 1989.
On the 89-95s you could simply disconnect the skip shift harness from the transmission to disable the system.
On 96-02 cars, which OBD2 emissions controls, it's not that easy because the CAGS is one of OBD2s monitered systems. On 96-up you've got to "fool" the engine controls into thinking CAGS is still functional. To do that requires installation of one of the so-called "GAGS eliminator" products available form Ecklers and other sources.