Need Axolotl Advice

My daughter has been researching Axolotl's for a while now and she came across a Craigslist ad indicating someone urgently needed to re-home their Axi. Being an animal lover, we decided to rescue it but were grossly unprepared for what we were about to get. The woman told me she had a tank and all the supplies needed. When we went to pick it up, it was in a bucket with just enough water to cover it. We took him home, rushed to the pet store and began buying all the needed supplies and asking advice. Needless to say, we were trying to keep him in a unestablished/uncycled tank and just do water changes frequently. He did ok for a week but then became sick last Saturday. I fridged him for what I presume was ammonia toxicity and he is doing well now, however, the tank is still not cycled (obviously), I am starting to use Seachem Prime and Stabilize today and doing daily tank water tests with the API master test kit. My question is (after this long, scary tale) should I just keep him in the fridge until the tank is safe to put him in (he's been there 4 going on 5 days now) or can I put him in a tub of water (with a fan to keep water cool) and do daily water changes until the tank is ready and then do the re-acclimation process by adding tank water daily in increasing amounts?? I am so grateful for this site, it has helped so tremendously and has saved our Axolotl -"Latte"from certain death!!

The latter is fine for the meantime, in a tub with a fan and daily water changes. It doesn't really take long to acclimate, you can do half/half tub/tank water for half an hour then it should be fine to go into the tank! As long as temps between the tub and the tank are the same, and pH mostly the same, it's fine to put the axolotl in. Once ammonia and nitrites are 0, and nitates are low (not 0), you're good to go!
Goodluck with the axolotl! Cute name!