Are you coming up through Whitehorse or from the West side through Tok? You won't need knobbies, particularly TKCs from Whitehorse on YT-2. It's a mix of Tarmac and hard logging road type material with little gravel. Even if you are coming from the Tok side it's really not bad. When I was up there a year and a half ago, it was raining like crazy and it wasn't bad.
On a side note you could ship tires to the Yamaha dealer in Whitehorse. My MT90 came apart outside of Whitehorse. I went to the Honda dealer (big mistake) and paid almost 300 bucks for a Heidi K60 and a sweet pinch flat 80 miles up YT-2 to Dawson. I have heard good things about the Yamaha dealer and they helped me out on my way home when I popped into Whitehorse after Prudhoe. The Alaska dudes will pipe up on road conditions. Srock