It sounds like what he needs is really clean water. Do a 100% water change, but keep your filter, it has benificial bacteria that'll keep your tank cycled. Make sure to dechlorinate it with your prime. Is he in a heated tank?
Don't worry about the water's ph. Chances are he's adapted to the ph, and so to move him to a different water source could amost be bad.
Believe it or not, he might not be that far gone. If his tail is disappearing, it is most definately just finrot due to bad water quality. If you do the proper ammounts of water changes to keep his water clean, he will heal. Believe it or not, bettas are tough little fish, and if you give him the right conditions, he'll get better.
Keep his tank heated from 76-80* F, keep his water clean and properly dechlorinated, if he needs to heal you might want to consider buying some aquarium salt and dissolving about a tsp of it into each gallon of water.
If you want to euthanize him, go to tropicalfishkeeping.com ,it's this site's mother forum, so you can log on as yourself. It has a sticky about how to properly put down a fish.