There are a couple of different ways to get the old gear lube out of a C4 rear axle and both have been covered adequately. I prefer the drain plug route, so a number of years ago, I modified the rear axle in my 95 with a drain plug.
As for the lubricant–I use Red Line Heavy Shockproof Gear Lubricant exclusively and I have used it for nearly 20 years. I run it 36,000-40.000 miles then change it. While Red Line Heavy Shockproof has a friction modifier blended in I usually end up adding an additional half to 3/4s ounce of friction modifier.
Because of common practice by dealers and service shops along with a healthy dose of Internet rumor, many people automatically use a "additive" in Corvette rear ends.
These "additives" are all "friction modifiers" which were originally intended to solve customer complaints of noise or chattering coming from the rear end during slow speed turns. The noise or chatter comes from the friction between the plates of the clutch-type limited slip differential used in C4s. The limited slip needs friction to work properly, but this friction can also cause noise (a sort of squealing) or in more severe cases, chattering.
The problem with these additives comes when they are misused. Most service shops and dealers, because they don't want to take the time required to find the exact amount of additive necessary to solve the problem, often ad a full bottle as a matter of practice during a rear axle lubricant change. Doing it that way doesn't get you the best compromise between friction and reduced chatter or noise.
Remember–the limited slip in a C4 needs friction to work properly so when you use a friction modifying additive you are degrading limited slip action.
What I do is: I change the gear lubricant, then I road test the car. I drive for 10 minutes on the highway to bring the lube up to operating temperature. Then I find a large empty parking lot and drive in slow, tight circles, one in each direction, listening for rear end noise or feeling for chatter.
If the limited slip chatters, I go back to the shop and add one ounce of friction modifier. Road test again. If the chatter is still present, add a second ounce then road test, again. If there is still chatter, add a third ounce. After the third ounce if chatter persists, I tell people they need to have the rear axle overhauled.
In the case of squealing but no chatter, I am very careful with any friction modifier because first and foremost, I want my limited slip to work. If the squeal is loud, I'll add half or 3/4-ounce of friction modifier and road test. If after that, the squeal is still present but subdued, leave well-enough alone figuring I've got the best compromise between low noise and high limited slip performance.
Lastly as for the choice of lubricants: not everyone is going to want the expense of Red Line's Heavy Shockproof Gear lubricant also some people are put off by the gel-like consistency of its calcium-based EP additive package and it's pink color. There are other Red Line gear lubes which have a more conventional consistency and appearance. Additionally, Driven Racing Oil (the consumer lubricant blending operation owned by NASCAR team, Joe Gibbs Racing) makes an excellent 75W90 rear axle lubricant for limited slip axles. For those looking for lower cost, you can use a petroleum-based gear lubricant but make sure it meets GL5 and is rated as 75W90 or an 80W90.
As for friction modifiers, the GM limited slip additive works well with most gear lubes except the ester-based products such as Red Line. If you use Red Line gear lubes, I'd recommend Red Line's Friction Modifier as it's compatible with all Red Line's gear oil formulae.