I'm not sure what the factory used. The service manual calls for their KP610-00250 sealant "or equivalent." The description on NissanPartsDeal says "gasket-liquid," which does sound like Hylomar, but it also says FIP, which I assume is form-in-place, which has me thinking silicone. Let us know what you find when you tear it down! I would expect either type of sealant to do the job provided it's applied properly and the mating surfaces are clean. Unless I had a good reason to use something else, I would use black RTV.
Seals are a good idea while you're in there. A seal that isn't leaking yet may change its mind after being disturbed. My front crank seal did that after a timing belt change.
I haven't opened one of these transfers, or dropped one on its own, so I don't have much in the way of specific tips. The shift linkage is removable, that might save you some trouble. If you drop the whole transfer case, a transmission jack will make your life much easier. You may need another jack to support the back of the transmission while the transfer is out. I would be tempted to try and remove the back case half without removing the rest of the transfer from the truck, if there's clearance for that vs the torsion bar crossmember. If you need to remove that crossmember, 1) make damn sure the front end is on jackstands first (the torsion bars hold the front end up) and 2) mark or take a picture of the adjusters before taking them apart. They're a bit fiddly to adjust, so having their starting position marked in some way will save you some time trying to trial-and-error it back to where it was.
Oh, and you'll need some way of getting oil back into it when you're done. A hand pump will do, slowly. I fabricobbled a jar with a hose and an air chuck to make it easier. When a friend and I dropped the transfer from an Exploder a while back, we overfilled it, installed it, then removed the fill plug to drain the excess. Worked great.