I think you should seriously consider dropping the barter system idea. Why?
First, lets define what do we mean by "barter system" - for the use of this answer, a barter system is one where you pay for some goods with other goods of any choosing agreed upon by the seller and customer. So, a setting where everything would be priced in water is not, in fact, a barter setting. Its just changing the currency from gold to another valueable resource thats hard to come by.
Barter is good for small scale tribal
A barter system is unmanagable with anything with complex production processes, high resource needs etc. To make something complex and time consuming, youll have problems in selling it for all the things you need. If a shirt, boots and pants are all made by different people, and together they hold a value of 1 horse, how do you sell your horse to get clothing? Especially in a situation where all the clothes produces already traded their goods amongst themselves, and the shoemaker already has a shirt and trousers?
More detailed example
To make a sword, you need to have lots of iron, time and skill. You need a workshop. Proper forging, heat treating and sharpening a blade are specialised skills, and in medieval many manufacturers specialised in only one of those. Other people mined the iron, other people formed it to iron bars. Now, how do you see paying all these people by one customer? Does he bring a sack of potatoes to pay for the sword? How are those potatoes distributed to all the people who took part in the production process? Who transports them? You may say that the blacksmiths buys the iron from the miners, The sharpener buys the blades from the blacksmith etc etc, you form a chain. Thats hardly managable and forms other problems. The merchant may accept payment in potatoes, but what if the blacksmith hates potatoes? Or has tons of potatoes already? If a sword os worth 3 metric tons of potatoes, how do you expect to pay for it in potatoes? No one will accept such a payment. On the other hand, if you have only a golden ring worth a whole inn, how do you pay for a one nights stay and a meal? What if no one wants your sword, despite the fact that making it is difficult and time consuming, an therefore the sword is worth a lot? If nobody needs it, its worth nothing!
Money is great
I have yet to see a working barter system or model. They cant really work, money is the great liberator. It eliminates so many of the mentioned problems. The big power of money comes from the fact that people believe it works. When everyone believes that he can trade gold pieces/skins of water/ printed paper bills for anything they need, they will be willing to give you what they got to sell in exchange for them. If there is no such belief, any form of advanced trading becomes almost impossible.
If you really want a barter system in your setting, accept the consequences
If you really want to go for a real barter system in your setting, go ahead. But know it will be very difficult to create civilized cities in such a system. Maybe in a primitive/tribal setting, where everyone is more or less self sufficient and there arent many items that need specialisation in order to be manufactured, and if so, they are extremely high in demand? (like medicine/healing services etc) In such a situation a specialist would be sustained by the society and offer his skills as needed (a doctor/shaman is worth being fed even if no one is currently sick).
So to answer the questions directly:
For example, how do I indicate that generally a sword is worth 3 skins worth of water but a dagger is only worth 1?
You dont. If using water as a currency, this is no barter system, just a currency different than gold. And if water is not the currency, you cant indicate how much a dagger is worth, as it depends totally on the need of the buyer/seller. If you last had water 3 days ago, youd give BOTH your sword and dagger for a single glass. People doing transactions with you will always take advantage of that. Your players will never be able to tell how much a beer will cost them and can they afford it.
Are there any systems with a similar mechanic?
There is a Polish system called Neuroshima, but first of all, it didnt use a factual barter system after all, and second of all, many players disliked that feature and made workarounds for it. The authors used a "virtual" value for items, called "gambles". There was no such physical thing, but it was agreed that one bullt 9mm is worth around 1gamble and most people used ammunition and medicines as a form of currency. I know of no "true barter" systems, as they cannot be actually regulated by mechanics, unless prices depending only on persuasion rolls and situational modifiers.