Hello Mate...It depends on the state of everything before you start. I quite like reusing the the existing haft if it is in reasonable condition. Always much easier to remove the old haft if everything is really dry.
I like to fit the haft and the wedge in very dry condition. Then stand the axe head-up. Pour a small amount of oil into the eye so it is soaked up by the haft and wedge. Repeat this a few times over a couple of days. From then on never let it dry out.
If you are removing the wedge but leaving the haft in...never soak before-hand. Everything will swell and you will never get it out.
You can accomplish more with a kind word and a pick handle that you can with just a kind word!