Bill, the skipping from 1-4 is called CAGS or Computer Aided Gear Selection. It's an annoyance that has been with Corvette owners ever since the ZF 6-speed transmission was introduced on the 1989 Corvette.
It does however, serve a legitimate purpose and that is to help improve fuel economy. There is a CAGS plug seal kit that you can purchase from aftermarket Corvette supply companies such as MidAmerica or Ecklers.
I do not have first hand experience at how the CAGS is wired in relation to the C5, but on he C4 generation, there are two pig tail wires that run along side the driver's side of the transmission case with a male and female end. You could unplug the ends and then use the plug seal kit to seal both ends to prevent dirt and moisture from entering. By disabling the connection, you disable the CAGS and can shift normally. Whether or not that is the same on the C5, I cannot say. It would be best for another member to help you out there.
Also, on the C4 generation of Corvette, you could purchase an aftermarket EPROM which you could get programmed to disable the CAGS automatically without having to unplug any wires. Companies such as Doug Rippie Motorsports and Lingenfelter Performance Engineering specialized in that. Again, whether or not something like that exists for the C5, I cannot say, but it's one more avenue you may want to keep in mind.
As for the "shifting into any gear", can you be more specific and provide more detail into the problem?