I'd 2nd use of copper wire, lots of gauges available from hefty 2.5mm domestic T&E down to fine or smaller 0.3mm for fine work. In a former existence I worked at Marconi's and guys would knock up incredibly intricate wire spaceframe models of cars and the like, in part to demonstrate their artistic bents but also their soldering skills!
I still tinker with IoT type projects and so still solder this stuff regularly with an ancient Weller TCP style 45W iron and if you keep everything scrupulously clean it's relatively easy to solder small stuff quite close without disturbing prior nearby joints and this is best done on a sacrificial scrap of Formica covered kitchen worktop, sure the bakelite or whatever surface will get marked, however it will withstand hours of use without catching fire and it's low thermal conductivity means you can with practice dip in and out swiftly with iron and flux cored solder and achieve surprisingly robust joints, it just takes some practice!
One of the challenges with modern components is the fact that most come in surface mount cases where the lead pitches are 1mm or less, and for than I have some reels of angel-hair 0.1mm polyurethane covered copper wire which is very tricky to work with and requires steady hands and very strong task lighting to achieve good results.
For a model ladder I am sure you can fabricate a very realistic ladder for your model, for sure it will be delicate but way easier to work with than for example piano wire, which because of the trace elements added to give it high tensile strength, they also tend to make it difficult to tin and hence solder.
Top tip if you are salvaging same domestic T&E is usually after stripping off the insulation you can easily straighten a length by clamping one end in a vice and the other with a single wrap coiled over some pliers is to pull it taught, and then marginally stretch it. because the wire is ductile it will 'give' a mm or two before reaching the snapping stage, and once the tension is relaxed the wire will remain straight even after the tension is removed,
Ed