Jennifer,
That is a lot of nursing when you're pregnant and tired! I don't have experience with this, as Lilah was down to two feeds with the odd mid-day feed very occasionally by the time I got pregnant (either time). But I'll offer what I did to get down to those two feeds. Lilah was nursing 4 times a day, first thing in the morning, after morning nap, after afternoon nap, and before bed (the classic EASY pattern) from 9 months, when we institued EASY to 12.5 months. A couple weeks after her first birthday, after she had started taking a sippy of milk (which I started by mixing half-and-half with drinkable yogurt, to encourage her to drink, then slowly reduced the amount of yogurt and increased the milk), I just skipped the after morning nap feed, gave her her sippy, and took her out to play. That last part was the most important-- the distraction part. She was much more fascinated with her friends (we live in student family housing and all we have to do is leave our apartment and go to the playground downstairs to find other toddlers to play with) than with nursing. I have read that this is the age at which that kind of distraction becomes possible, becuase they are suddenly much moe interested in what's going on around them. A few weeks later, I did the same with the after afternoon nap feed. We kept up with morning and bedtime nursing until a couple weeks ago, when we started dropping the morning feed. We are now dropping the bedtime feed. She hasn't nursed at bedtime for three nights in a row now, so we might be done.
Anyway, I don't think you need to worry about the sippy too much yet, though you might try to get him used to it so he can take milk from it when he needs it. If you are still nursing 3-4 times a day, he will likely just nurse longer and take more at one nursing, and he really will not need any extra fluids (except for maybe a sip of water now and then). As long as your supply keeps up, he'll be getting all the fluid he needs from 3-4 feeds, and a good deal of the calcium and protein he needs (though supplementing with yogurt and cheese will help with that). So I'd advise not pushing the sippy during the nursing times you're trying to drop, and just doing an activity during which he does not normally nurse, like going to the playground, a play date, etc. And encourage the sippy use at other times, so he doesn't associate it with a nursing replacement. Does that make sense? And of course, don't try to drop more than one feed every four-five days, or your breasts will be near to bursting!
It's also likely he'll drop one of his naps sometime fairly soon, which will then require reworking of the nursing schedule anyway. That might also offer another opportunity to drop a feed.
HTH!