TL;DR: the smallest possible hegemonic economy would be one the size of the international economy, because it provides the international currency.
One can consider the possibility that a relatively small country, like Switzerland, might develop the hegemonic currency (the currency in which international trading is done by default). A big part of the hegemonic currency is trust. So if the small country is trusted, it might also be the currency hegemon.
There is a big challenge though. How do you get the currency out to other countries? As the international market increases, it requires more and more currency. How do buyers get the currency in the first place? Traditionally there have been three ways to distribute the currency:
Loan it. Obviously this is only a temporary solution, as repayment of the loan with interest requires even more currency. May work in the short term (decades) and lead to instability in the medium term.
Give it away. International aid can transfer money from the hegemon to other countries. This can cause strain though, as popular (democratic) governments don't like giving away their money.
Trade deficit. If the country runs a trade deficit, it can send out money in exchange for goods.
The United States mostly engages in the last. It runs a trade deficit equal to about 2.5% of GDP per year to fund an ever-increasing pool of its currency that is used in international trade. But this too causes economic strain, as it makes it harder for the US to export. Also, cheap imports compete with domestic production. The trade deficit itself becomes a political problem. For a small country (say a fortieth of the size of the US), the trade deficit could be as large as the whole economy.
Another side effect is that internationally, dollar-denominated investments are favored. So the US has become a debtor nation. Other countries loan their dollars to US borrowers and buy up US stocks and real estate. That sort of works with the US, as the economy is bigger than the international economy. But with a smaller country, the entire country would be owned internationally.
For a small country, there is a limited amount that can be owned. Eventually people would not be able to invest their international currency holdings in the only country that is guaranteed to use that currency.
Loans aren't sustainable. They create a positive feedback loop. To pay off the loan, more money is needed, which can only be obtained by a new loan. So the loans can only grow, never shrink.
A trade deficit is not sustainable. Eventually the country can't reduce domestic production anymore. Its entire economy would be based on imports. All its businesses would be owned by foreigners.
That leaves giving it away, which is unsustainable in a democratic country.
The net result is that the only stable hegemon would be a monarchy. It would import everything and engage in global public aid. Perhaps it would control all the libraries and museums of the world, an Andrew Carnegie government. Its consumption would be determined by the size of the international economy. Or conversely, the size of the international economy would be limited to its consumption.
Of course, you may not want a stable hegemon in your story. Perhaps your story is about how the distribution methods fail over time.
It is possible that the US is too small to maintain the hegemonic currency. It is already feeling economic strain from having a trade deficit of only 2.5% (stable for ten years) that was 6% in 2006.
You might also consider the number one reason why China does not take over currency hegemony from the US: it doesn't want to be consumption driven. China wants to be production driven. But that doesn't work with currency hegemony. Currency hegemony forces a country to be consumption driven with large imports. It's unclear if the European Union's currency area is willing to be consumption driven either. It's dominated by the people who ran the German central bank. Germany was and is production driven.
That's what you have to write into your story: reasons why the larger economies would not take hegemony from the smaller hegemon. Perhaps they prefer to be production driven. Perhaps they can't agree with each other. None of them like the hegemon, but the thought of one of the others in that position is scarier. So the current hegemon stays the hegemon as a compromise. Because the larger economies are capable of breaking the hegemony, you have to explain why they don't.
