If you dig into what was going on in the Mediaeval period (and before and after as well) you'll find that the colonists will simply fit right in and merely need to develop a reputation for honoring their debts.
Basically the currency situation was more complex than you might think. Minting coinage is actually pretty expensive, and most kings at the time tended to do it as little as possible. And yet recognizable coinage of known purity and weight makes trading outside of the local area so very, very much easier...
So there ended up being quite a lot of stuff in use. Gold was a good way to transport money over long distance due to its very high value per unit size and weight. At the same time though, it's so very valuable that using it for everyday transactions would require some very precise measuring equipment.
So there ended up being quite a bit of silver coinage as well. It's bulkier for a given amount of value, but that makes it easier to count for small transactions.
But... The minting process is expensive. So the king (and occasionally some merchants) tended to mint enough gold and silver for their own purposes, and that was it. It wasn't really enough to conduct day-to-day trade for everyone.
Which is where a lot of the copper coinage came from. Copper is even bigger and bulker per value than silver, but there are also a lot more copper mines, and if you're mining and smelting the stuff anyway that significantly reduces the cost of striking some portion of it into coinage. So copper tended to be locally struck in areas with copper mines, and how far it spread from there depended largely on the reputation of the people doing the minting. (Which is the same as for the king's gold and silver. Yes, they could debase their currency, but if they debased it too much more than their rival kingdoms people tended to figure it out and would trade the debased coinage at a discount to match.)
But what if you weren't near a copper mine? Well, metal isn't the only thing with value. Various non-perishable or, at least, long-lived foodstuffs also make decent money. But they're even bulkier than copper, and easier to damage, so nobody really wants to carry them around all the time.
But it's also far more efficient to build one, giant granary that's sealed well enough to keep the vermin and moisture out than it is for everyone to build their own, tiny one. So when the farmer brings his harvest in, it's just going to get poured in with everyone else's and he'll be given a chit for how much he's allowed to withdraw. (There were a number of ways to do this depending on the literacy level in the area and the expensiveness of various types of bookkeeping materials.) It was not uncommon for these chits to become recognized as currency and used for trading in the local area. So the idea of tokens that represent value rather than being value is something the natives will already be used to.
The part where you're going to run into trouble trying to introduce chits that don't have a fixed backing is trust. If a chit is worth a certain amount of grain or gold or silver or salt or whatever, that makes it really easy to tell if the person issuing them is cheating you. And the standard penalty in the mediaeval era for fraud was to draw and quarter the perpetrator. Obviously this didn't generally apply to the king, but even he had to be careful or his political rivals would use it to gather support, and that could end very badly indeed...
So the fiat currency you're trying to introduce will be accepted so long as the prices of the goods the natives want to buy from you remain relatively stable. But the number one reason governments want fiat currency instead of commodity currency is so that they can arbitrarily create and spend as much of it as they like... Which leads to unstable prices... And then they use threats of violence to force people to keep using it anyway. Since you've stated that that kind of methodology is off the table for use with the natives, you either effectively bind the value of your "fiat" to the commodities you're trading, or else the natives will simply quit holding it in their cash reserves. They'll just spend it immediately for durable goods or commodities that they can trade using their own money (or potentially will become their own money) and the cost of any inflating the colonists' distant, central government does of the fiat supply will be borne solely by the colonists...
Which... Historically that kind of crap ends up being grounds for a revolt since it's effectively a hidden tax...
In short, the advantages of "fiat" money are not the same as, and do not benefit the same people as, the advantages of "paper" money. And the natives of a world with a fractured, feudal society are not as abstracted from their money supply as we are today. So while convincing them to accept the latter would be relatively easy, convincing them to accept the former would be -- at the very least -- a generations long process. But it could also give rise to interesting plot points for your story.
If you want to make currency a central point in your story I'd suggest reading the sections of "Human Action" by Von Mises which relate to the different traits and attributes of money and the effects of credit expansion and currency manipulation. This will give you a good grounding for sorting out how the clash of the two cultures will sort itself out.