I had an idea to take my Lan Lan 4x4x4, and mod it into the shape of a sphere. (My first shape mod) I have already took off the stickers and have started sanding the sides down with the Dremel. I have actually no clue what i'm doing, i'm just using common sense.

Good luck, itll be easier with a belt sander id say because you have 2 hands on the cube and get a nice smooth type sphere shape

I don't know the mechanism too well but if you continue I am 95% certain you will destroy the puzzle. I do however admire your approach and only wish other newbies were brave enough to give this kind of thing a go. It will be a great learning experience.
My advice btw is-
1. Before you go any further build up all 24 middles.
2. Continue using a Dremel but as you get further alternate between scrambling the puzzle and Dremelling.
3. Watch my 7x7x7 Ball construction video.

Thank you for the advice! The video helped me out alot!

How do you ensure that the puzzle does not become offset when cutting it down?

Tony you probably dont know exactly how many hours for each step it took to make since it was so long ago but how long would you say it took to make excluding stickers?

Although I didn't explain, this is how. In fact making a twisty puzzle into a perfect ball is a lot times easy than a solid piece of wood for example (assuming you didn't use extra things jigs, lather etc). This of course assumes the puzzle can take such a cut down. Many won't and you hit crucial mechanism parts before you reach a ball shape.
Unfortunately I fear TimmyCuber98 is going to run into major problems if he simply continues.

I know the stickers took around 8 hours but I'm not sure about the puzzle. At a guess I would say maybe 15 or 20. The actual shaping is quite quick but filling the parts and final sanding takes a long time. At some stage it has to be taken apart and each piece cleaned and given a rounded edge.

Great mod

Good luck! As Tony said I think you will hit important mechanisms before you get this into a sphere. Im interested to see if you manage to get it working.