There's no such thing as a fish for cycling. For fish-in cycling, you pick whatever fish or aquatic critter you will have and you monitor the water daily or twice daily. You then do a water change whenever the ammonia reaches .25 ppm, which could be once a day, every other day, or could be several times a day depending on the creature and the size of the tank. This could take several weeks for the cycle to build up and hold. If you do not monitor the ammonia closely it could harm or kill your critter.
Some people recommend keeping the axolotl in a plastic tub, like a sterilite tub, food grade preferred. Something that's easy to change the water daily, not as much water. It's also easier to have 2 containers, and just move your axolotl from the dirty one to the new one instead of changing the water in it's tub.
A liquid freshwater testing kit is recommended for reading the parameters, and Prime is also recommended as a water conditioner, especially while cycling.