I'd MUCH rather install the L/S (limited/slip) differential, in your situation, than swap out a set of ignition wires on an LT1.
You will benefit from having/borrowing/buying a magnetic base "plunger type" dial indicator, but otherwise, no special tools are required.
Pull cover, slide out both axles, check gears for wear pattern, and if good: measure backlash (will likely be around .008"), then re-use the same gears.
Swap ring-gear & bearings if good onto the new 9C1 diff., install the unit with proper side to side bearing pre-load (about .020" total) & duplicate old R&P gear back-lash setting.
You can optionally re-check your gear pattern with white or yellow gear marking compound.
You will probably need to play "musical side-shims" to achieve the correct side pre-load value and B/L settings.
Include a .010" shim in both left & right shim-packs, so that you're able to slip the ham in and out easily (@ "zero" pre-load) until B/L is spot on, then add .010" back in on both sides, to achieve good side-bearing pre-load.
Slide back in the axles, cross-pin & horse shoe "C"clips, cover w/gasket, and re-fill housing with lube & L/S friction modifier, basically thats it.
Because you are re-using the same gears back in the same housing, its WAY simpler than a full-on R&P gear & L/S change over.
I would also install a new pinion seal in there, just on general principles, for insurance. While the "ham" is out, you can turn-feel the pinion bearings and pre-load there as well.
Go for it, its a lot easier than it sounds.