Matt has asked me to post my results, so here they are.
I had poor execution. If one is easily saddened or depressed then stop reading now.
I set up a 5 gallon tank outside. Attached filter to ensure water circulation so the heat would drop evenly throughout and used a separator to divide the tank in half. Additionally I put a dripper that would drip alcohol in at a very slow rate. I also had slushed water ready just in case, and a tub of ice cubes.
Then I went to my old tank. The Betta was lying on the side just breathing, old and blind. As I made my resolve to go on with it, I reached out for the Betta. I do not know what it was but he would shy away from my hand. He would try hobbling away from my hand with whatever strength he had left. Still I ended up grabbing him and transferred him to the outside tank on one half of the divider.
Water temperature was 27 degrees. I would drop water cubes on the other half of the tank and let the filter distribute it. Temperature would drop one degree every ten minutes. When it reached 23 degrees I noticed that my Betta started moving sideways. At 20 degrees the Betta was actively swimming around. At 19 it got frantic.
That's when it hit me. This is going to be too long and painful for my Betta. I prepared ziplock bag, reached in, Betta instantly darted for my hand(still swimming sideways, almost upside down). I grabbed my Betta and dropped him into ziplock bag.
That was the most gruesome part for me and I broke into tears. For roughly 20 seconds or so (felt like an eternity to me), the Betta was darting very frantically everywhere in pure shock, and maybe even pain. Afterwards for the next 5 seconds seems like Betta realized what happened, slowed down, gills opened up and Betta sank. Not upside down, just sank... No more breathing...
Then I buried the Betta with the ziplock bag (it is cold, so Betta would not wake up again), said a prayed and spent the rest of the day in pure silence and sadness.
If anyone ever plans to use alcohol and ice method, be warned. Fish will be in hell for roughly 30 seconds before falling asleep.
Hope this helps someone someday.