It is pretty much a drain and fill procedure. While the manual procedure doesn't say it, many TSBs for different procedures talk about premixing the fluid and additive outside and then filling. Think following the manual would work fine.
Quote:
Lubricant Change
Draining Procedure
1) Raise and support the vehicle. Refer to Lifting and Jacking the Vehicle .
2) Clean any dirt from around the differential drain plug.
3) Position a drain pan under drain plug.
4) Remove the drain plug from the differential and drain the fluid.
Filling Procedure
Notice: Refer to Fastener Notice in Cautions and Notices.
1) Install the drain plug to the differential.
Tighten the differential drain plug to 35 N·m (26 lb ft).
2) Clean any dirt from around the differential fill plug.
3) Remove the fill plug from the differential.
Important: If equipped with a limited slip differential, limited slip differential lubricant additive, GM P/N 1052358 (Canadian P/N 992694) or equivalent must be added first. Refer to Lubrication Specifications . Approximately 0.23 L (7.8 oz) of residual fluid will remain in the differential.
4) Fill the differential with 75W90 synthetic axle lubricant, GM P/N 12378261 (Canadian P/N 10953455) or equivalent. Refer to Lubrication Specifications .
5) Inspect the gear lubricant level to ensure it is even with the bottom of the fill plug hole to no lower than 6 mm (0.25 in) below the opening.
6) Install the fill plug to the differential.
Tighten the fill plug to 35 N·m (26 lb ft).
7) Lower the vehicle.
The service manual spec for the additive is different then the owners manual quanity. For a fluid drain through the drain plug, it shows 2.37oz of additive with 1.06qts of lubricant.
The thumnails are, drain on left, and refill on right.