1981 owner ~ Welcome to the Corvette Action Center Community ~
I changed out the speedo cable a few years ago. As I recall it wasn't a real cuss invoking experience
I did take the driver seat out to have more room to work.
Some folks lower the steering column, I didn't and still had no problems getting the Speedo/Tach bezel off or access the screws, but I don't think you would really need to move the speedo out a bit to access the Cable, you might be able to access it from under the dash.
The cable is NOT screwed onto the back of the speedometer, it has a clip type thingy. Once you get it loose from the speedo housing... I taped the new cable to the old one and pulled it through the firewall with the old one attached. I destroyed the firewall rubber gromet in the process, (got a new one from local Chevy Pars) ...
Mine was a ONE peice cable (4-speed no cruise control) then I went under the car and removed the cable from the transmission. There should be a aluminum support that attachs to the cable and bolts to the transmission for supporting the cable. Before I pulled the cable out from underneath the car, I taped the end of the New Cable to the old end and pulled the new cable down around the same path as the old cable while pulling out the old.
Then it was put the support bracket on the new cable and install in the transmission. Back up topside and installed the cable in the back of the Speedometer.
I did have the old speedometer out as I was installing a new 140 mph speedo so that is why I stated about taking the Bezel off the Speedo / Tach and access to the mounting screws for the Speedometer.
Even if you need to do that, it wasn't that difficult. Oh and while I was there I changed out ALL the light bulbs with 7watt, factor yare a lot lower, I don't recall the exact wattage, nor do I remember the 7watt bulb #'s its in a post about RARE In Phase I or II if you do a search for Rare in phase that should get it
if not and you are interested let me know and I'll find it for you.
Good Luck and remember it will bring you closer to your C3, I call it Bonding, some folks call it worse
hnoes
Bud