150 grit is perfect (I use 120-180 for all corks). I do not like to sand corks with them on the instrument, as I do not like to accidentally sand the tenon lips. I have done it carefully when it was the easiest route, but instead I like to use a vernier caliper, and make sure whatever cork I need has been sanded, beforehand, to the thickness I project. To do this, I drag the cork I have just cut backwards across a quarter sheet of sandpaper in one consistent movement, over and over, and then I reverse the direction to get the other end. Cork is fragile when tugged on, but you will develop a technique for it.
Every tech has a different procedure, but I do not much care of this bloke's method for cork removal. If it works for him, great, but I will not follow suit. I know a tech who uses a lathe and a chisel bit--a technique I am even more averse to. It is also not necessary to remove keys to remove that middle tenon cork, as he stipulates. Toothpicks are a great tool for spreading contact cement in difficult areas such as this, and then the new cork can be slid behind the keys quite effortlessley. The same can be done with sandpaper. I typically start cutting off cork to be replaced with one diagonal slice across the short run of the cork with a small Exacto blade, and then gently lift up and away with a very small screwdriver. Once I have the cork cleared, I soak a small section of cotton rag in acetone, and rub it across the tenon to rid it of the contact cement. Shellac requires more effort, but the same same technique is used. Old shellac is a nuisance, and often takes root in the tenon grooves, making removal more time consuming and fidgety.
For your immediate needs, if you cut a 10-12mm strip of sand paper, you can wrap it round the tenon, and carefully sand it out, back and forth. Keep in mind that trying to sand cork that has recently been greased is like trying to sand silly putty. It is slow going and frustrating.