No waterer to be found and chicks due any day...

I would just make due with what you have until they come in.  Just a shallow bowl, like you said would suffice.  It doesn't have to be anything fancy.

If it will hold water, you can make it work. That means a saucer, that feeder, or about anything else. They will still get it dirty. They will scratch stuff into it and they will sit on top of it or next to it and poop in it. Be prepared to change out the water regularly. And keep them enough water so they don't run out.

I can think of a few reasons the feeders are not regularly used as waterers. Waterers especially designed to be used as waterers and to hold a lot of water are usually available. Those feeders would be hard to handle full of water. You'll spill it and make a mess. A waterer needs to stay level. If it tilts, it can spill. They can and will turn it over by playing on it. Maybe you can see how I handled that for my feeder in the photo.

I've never used 'chick' sized waterers, the 1quart size, for our chicks....just the 1gallon sized one.  It works very well for the first week.  2nd week, I put it up on a 2x8" scrap of wood to get it off the floor of the brooder/coop (chicks kicking shavings into it).  3rd week gets a thicker brick to keep it up a bit more.....and then they're outside in a tractor or with Mom in the big run.  I've got 2gal waterers, 5gal waterers and a few 1gal waterers spread about. 

I vote for the regular sized waterer. You won't have to buy another later or be filling it too often. Do give them fresh water every day. If the dish is too large and you worry about someone drowning put some marbles or rocks in it.

Yep, just get a big chicken waterer if you cant find one for chicks. They use them just fine.

Either a shallow dish with rocks in it or a 1 gallon waterer would work fine.  Sometimes I use the chick waterer, sometimes the 1 gallon.  Depends on how many chicks I have.

The chick waterers are so low that they often get poop in them. While I've never brooded more than a few chicks at a time, I've used things like cottage cheese containers or even (slightly low wide) coffee mugs, which are tall enough to be above their butts, but low enough to get their head into.

 

If you are getting a lot of chicks and have space in the brooder, use a full size waterer. If not, put a few smaller containers around. (It's good to have more than one so they can all access them and in case they tip one over).
 

As long as the top of the sides are lower than it's back they can drink out if it. They will get less foreign material in the water and feed too if they are elevated.