My daughter was breast fed for 23 months. She was exclusively breast fed for the first 6 months and then we slowly started replacing breast feedings with solid meals. I never used a bottle, so she transitioned to a sippy-cup really easily. I picked which breast feedings to replace in a way that would still give my body a regular production schedule. Beyond that, I pretty much let her call the shots. We replaced a couple of feedings with solids and then she let us know when she wanted solids at other feedings and we slowly switched everything in. It worked well for me too, because my body got regular scheduled signals about how much milk to produce, so I wasn't struggling to produce, or overproducing and having to express to relieve discomfort. By the time she was 23 months, she was more interested in toys or books at bedtime that she was in having her "night-cap" so we skipped one night to see what would happen, and she just never asked for it again.
I know that this is not how it works with every child and that there are always exceptions, but I do think that if you let them call the shots to an extent, they will let you know when they are ready and comfortable with giving up that last feeding and it's less stressful for everyone. No sleepless nights with howling upset toddler! :)
Is there a reason you have only 3 weeks? If this is just a desired timeline you are setting up for yourself, and there is not an event or health condition etc. necessitating this change, you may want to let him hold onto that last feeding for a little longer and let him tell you when he's ready to call it quits. I wouldn't go every-other-night if you do decide it's time to cut it off. This will be a irregular and uncomfortable schedule for both you and your baby. If you don't already have a bed-time routine that involves a book, it may be time to start. If he knows that he gets a book and a sippy-cup with milk at bedtime, he may not even cry for a breast feeding, and you can wipe his gums and teeth down with a warm washcloth after he's finished. Snuggle him nice and close while you read, because the need for breast feeding is as much a "contact with Mommy" issue as it is a food issue.
Hope that helps. Best of luck!