We weaned the before nap bottle at around 16months and the BT bottle at around 19months (same as you). I reduced the amount of milk over a couple of weeks from 200ml down to 100ml. Then one day when he was in a happy mood about going to bed, quite tired, big morning and exhausted I just did his stories and didn't offer the bottle. He didn't even notice!
We did the same with the BT bottle later. When we were reducing it and he complained about being finished I would just say "thats all the milk, you must have drunk it all up" and he would look at the bottle and be like "oh yeah theres none left now, ok"