Welcome aboard, Denise! Seeing a Disney cruise through the eyes of a two-year old is such a magical experience! I hope you'll have your camera with you at all times when you're sailing, as you're going to be creating such magical memories!
Buzz and Woody are known to be on the ships at times, however you didn't mention which ship or itinerary you're sailing. Since you noted in your details that you set sail June 1, I'm going to assume you're on the Disney Dream's four night sailing. If that's the case, most likely Buzz and Woody will not be onboard, though characters are always subject to change. Those favorite Toy Story friends haven't been listed on the recent Disney Dream character schedules I've seen in the Personal Navigators, but you never know, there's always a chance.
The good news is that the
Dream's Oceaneer Club has some really fun play spaces, including Andy's Room from Toy Story, where your son can play with a life-sized Mr. Potato Head, climb through Slinky Dog and hang out with Rex! Though he is two young to stay in the Club for the secured programming times, there are Open House hours offered each day when parents can stay and play with their kids of any age in the club. So, keep an eye on your Personal Navigator which will list each day's Open House hours. Then, head in there with your little guy and join him in the fun of exploring Andy's Room. He'll become toy-sized himself, so it makes for a lot of fun!
I hope those details help, Denise! Enjoy your cruise!