Hi Mark. Such good news overnight with the confirmation from the Japanese PM on the intention to open up to fully independent travel again in mid-October, hoping to see the documented confirmation on that next week with it being a public holiday today.

While the New Years' holiday is a popular time for people in Tokyo to visit family and hometowns, it is generally only for a few days. You don't seem to notice large numbers absent from the city in the week leading up to it. Hyperdia (the best public transport planning app) has gone offline this month so using Google Maps is currently the easiest planning tool. You don't mention where you are staying but Tokyo Disney is away from the major commuting direction. Where you are starting will determine which subway lines you will use, in the morning I'd normally avoid Ginza and Marunouchi lines during the peak but say you were staying in Shibuya for example you would use less busy lines anyway and not pass through the central city stops so it will likely be more crowded than at other times of day but OK.

I'd use Google maps and put in your hotel or intended station with the destination of Maihama Station (the Disney Station). You can put in the arrival time you want at the station, from memory Disney opens at 9 and it's a little walk from the station to the gates. What a fabulous time of year to go, enjoy!