If the old ratio was 3:55 or less, you will probably only need to make the easy change.
You need to measure your speedometer error first, which can be done by setting a constant speed on the freeway such that the mile marks go by at exactly one minute apart (you are exactly at 60mph) and note the reading on the speedometer. Then pull the plastic "driven" gear currently in the transmission and count the teeth and check the color of the plastic (to do that, remove the speedo cable from the transmission, then a bolt & retainer, and use a screwdriver to gently slide out a fitting, shaft, and plastic gear as an assembly). If that plastic gear has 21 or fewer teeth (possibly 22 teeth IF the plastic gear is silver-colored), you can make the simple driven gear change.
By using the ratio difference between the indicated speed and the actual speed (60mph) divided by 60mph, you can figure out which gear you probably need... if you have a 20-tooth (blue) gear and the speed difference were 10% (ie, 2 teeth), you will now need an 18-tooth (brown) gear. The brown 18-tooth gear is the gear normally found in a 3.08 ratio car, but tire size can make a difference.
Vendors like Corvette Central sell the gears for about $9 each.
If your differential was formerly 3.70 or higher (numerically), then the steel drive gear inside the transmission has to be changed, also, which is a lot more difficult... I think the tranny has to come out to change that one, but I haven't changed one.
There are also aftermarket adjustable cable gearboxes that can be "spliced" into the cable under the dash to allow you to alter the speedometer reading, but it would be relatively expensive (maybe $50 to $100, yet still cheaper than tearing the tranny apart).
If you haven't already noticed, the tachometer needle pretty much parallels the angle of the speedometer needle in 4th gear... you can judge your steady-state speed pretty accurately by simply mentally superimposing the tach needle position onto your speedometer (or make some marks with a grease pencil on the tach face), and thus you can get along pretty well without a speedometer.
