To push the food down the gullet you have to take a drink for the simple reason that the swallowing muscle does not do its duty and the food gets stuck. To avoid arguments in a restaurant when you need something to drink, why not ask for a small bottle of apple juice, room-temperature.
Any cold drink makes the swallowing muscle go into spasm.
That not only hurts a lot, the muscle can take a rather long time to come round again. If the reply is that the apple juice is only available from the fridge, you can nicely point out that a bowl of hot water to put the bottle in will do the trick. Typically these heaters, which last for hours, are placed inside mittens by cross-country skiers and others who enjoy winter sports. Boot-heaters are also available. To find these products, inquire locally or search on the Internet.