Nevermind then...I'm in SoCal...haha

 

I would say to start with polish. Use that first on a test section and see if it removes enough of what you have going on w/ the paint. Using a less abrasive product is always a good idea, especially if it'll get the job done. If using just the polish doesnt work, you can then step up to the compound. Depending on how bad the paint is, it may require more than one application of compound. However, if its just some light/medium stuff like you mentioned, one pass is probably going to do it.

 

I would also suggest trying out a clay bar first. You can do an over the counter brand, or, we have a clay package put together which has a large, 200g bar, clay lube and storage container for the clay. Check out this kit here: http://www.glimmerglassdetailing.com/20clbarlupa.html
Like I mentioned, it has a large, 200g light clay bar, LUBER clay lube and a flip top box to store your unused clay in. You can tear the clay in to smaller pieces, this way if you drop it, or if it becomes too heavily contaminated, you can just grab another piece w/o having to worry.

After claying, you might consider going w/ a paint cleaner.
I would say to go w/ p21s paintwork cleanser

 

The problem I usually see w/ scratches in vinyl is that they cant be polished out like paint can. Since vinyl has a texture to it, as opposed to a smooth surface (like a clearcoat), when you try to level the scratch to remove it, you wind up smoothing out the surrounding texture and changing the appearance.
Now, with that said, I've taken 0000 steel wool to some interior panels w/ similar scratching (although a little less apparent) and done some minor smoothing to help reduce the appearance of the scratch.
It may be a better idea to just replace the one section of the door sill. I would think you could find one at a relatively inexpensive cost.

 

Thanks a lot chris, I will try that out

 

You got it bro! Lemme know if I can help out w/ any other questions.

 

Do I just use the steel wool and rub it on the scratch? No other solution required? Is there any other alternative?

 

When I use it on vinyl, I use it dry. Unfortunately, I dont personally know of many other ways to go about it. Like I mentioned, scratches on interior vinyl pieces is really tough to clean up b/c of how it affects the surrounding area.

Have you tried a dash/vinyl protectant yet to see if it helps to mask the scratch at all?