Welcome to the forum, Heinrich.
No, you don't need a second disk. The T2 is specifically designed for chefs like you. It is designed to be a complete unit in itself, not needing any accessories or extra disks (grinding wheels). All diamond wheels are a little more coarse than rated for the first few knives. This is perfectly normal. After six or eight knives, your wheel will settle in to its rated coarseness. Use very light grinding pressure all the time, especially during the break in period. Your diamond grains are very sharp; let them do the sharpening.
The standard grinding wheel for the T2 is designated DWF-200. (Diamond Wheel Fine, 200mm diameter, 600 grit). Presently Tormek only makes one extra wheel for the T2, the DWC-200 (Coarse, 360 grit). During development, one of Tormek's major customers in Sweden requested a more coarse wheel. Tormek originally planned to offer only the DWF-200. If you sharpen your knives regularly, you will not need the coarser wheel.
If you have not already found it, Tormek has made an excellent in depth video on its you tube channel. Like all of its online classes, there are versions in Swedish, German, French, and English. I highly recommend this video.
Please keep us posted.
Ken