Ok OP, I was at the park today for a reason on a different matter and parked in the Toy Story parking lot! And when I came back from the park, I decided to take a stroll from the parking lot to Sheraton and it honestly took me 5-6 mins tops, from the drop off/pick up area to Sheratons main lobby! Yeah VERY fast! Now I'm somewhat of a fast walker, but honestly even if you add a few minutes, it will still be less than 10 from the lobby. And I did see the shuttle stop at Sheraton as well. Obviously very close, like right outside the lobby door BUT A. I never seen it come the 20 mins I was at Sheraton although it couldve came the mins I was indoors and B. Something I didnt think about but you will probably be making quite a few stops at other hotels before you even get to DLR. TS shuttle, its a straight shot, 5 mins there, busses ALWAYS leaving every few mins and most importantly its FREE!!!
So its a no-brainer, at least for me when I stay there this week!