Fixed output TRIAC dimmer style circuits to run 115V heating type appliances on 230V, mostly for the travel market used to be fairly common, so, ignoring the safety issues, there is nothing fundamental that prevents it being converted successfully- its just a matter of limiting the max. power to the element to be no greater than its maximum when running from 115V. However simply swapping one resistor is unlikely to be the solution, because a 230V version of the iron, although it might use the same dimmer PCB with a few component changes, it would almost certainly use a 115V element.
However in real life one *MUST* consider the safety issues. If you were going to attempt to modify it, the first thing to do would be to check if it could be done safely. Start with a 1KV Hi-Pot test between both pins of the mains plug shorted together and the shaft. You are looking for a high insulation resistance - tens of \$M\Omega\$ when cold. Then heat it up to max on a 115V supply from a Variac or autotransformer, to max temperature and immediately reconnect it for the Hi-pot test, monitoring the resistance as it cools. If it drops below 2\$M\Omega\$ at any point, or flashes over, that's a fail, as the limit for a class 1 handheld heating appliance is 1\$M\Omega\$ at 500V and you need a safety margin, hence 1KV and 2 \$M\Omega\$. A low voltage insulation test is inadequate as you need to know if the insulation will withstand 1KV safely before connecting it to a 230V supply, and cant reasonably disassemble the element to check insulation types and thicknesses, and creepage distances. I'm expecting it to fail the high temperature Hi-POT testing . If it passes, you've still got to sort out adequate grounding for the shaft that wont be compromised by the possible high temperatures, and will remain attached even if the shaft starts to come loose from the handle.
Next would be to run it with the temperature control board removed or bypassed, and a 1.5A 250V fast blow fuse in series with the element, on a 230V dimmer running from an energy meter, and soak test it at 60 watts for a couple of hours. Let it cool off a bit then briefly connect it to the full 230V supply. What you are checking is whether the element's insulation can withstand 230V across the element. If you are unlucky, it may flash over and take out the fuse. If you are really unlucky it may take out the dimmer as well.
You can now start reverse engineering the power control board, checking creepage distances and deciding what component changes will need to be made to make it safe to run on 230V, to limit the power to 60W max, and to give it an acceptable control response.
Anyone competent to do the above will realise there's many hours of work involved, and no certainty of a usable iron at the end of it, so its just not economic for a piece of cr@p firestick maybe worth $10 bucks.
*ALWAYS* be suspicious of 'free gifts' - TANSTAAFL applies!
