You can put the aquarium salt in the big tank...just put 1 tsp for every gallon. So long as you don't have cory's or other scaleless fish in that tank..everything else should be fine with it in there.
There really is no need for a salt bath for a split fin. Usually salt baths are reserved for more severe cases where the fish has fin rot.
Salt baths are complicated and stressing, so should only be used in serious situations. As you have to gradually add plain water back to the heavily salted water..to keep your fish's cells from intaking too much water all at once (the salt squeezes the water from it's cels during the bath...sorta like dehydration) and if you do not do it correctly..it can kill your fish. So you can't just stick your fish in a salt bath then plop him back in his tank.
I would get some Melafix and add to your big tank...I have 3 fish that came in with damamged fins (from rough handling during shipment) and 2 out of 3 have already repaired themselves..the 3rd is going to take some time..as a complete chunk was broken off.
Or just buy a gallon tea pitcher and medicate him in that for the 7 days that is recomended if you don't want to treat the entire larger tank.