Hi, Ryan.
Hope you don't mind me jumping in here, but I think the BEST thing you can do is to get the paint tested for lead--and you can do it yourself. Try your local hardware store, or maybe safety supply house and get a lead test kit. Typically, the kit consists of a pad that is saturated with a chemical compound. You rub the saturated pad on the paint, and if lead is present it turns pink or bright red. If no lead, then there is no color change.
If no lead is present, have fun in the restoration.
If lead IS present, then the only thing I can tell you is that the effort needed to perform a restoration and keep contamination down is going to be very prohibitive, and somewhat problematic. All work will have to be done using wet methods. No dry sanding, grinding, or chipping is allowed. The only recommended way to remove lead paint is through a chemical strip, and that will have a negative effect on your work since the substrate is cardboard. Even a wipedown to remove years of collected dust should be done wet., since the dust will contain lead. Do NOT use the household vacuum cleaner to do any precleaning. And any cloths or rags used for cleaning should be thrown away when finished--don't wash them with the family laundry. You may want to give serious consideration to wearing some disposable coveralls to avoid getting lead dust in your clothes.
It may be that the best way to proceed would be to work the model with the paint in place. Make sure you wear gloves, and a respirator equipped with HEPA or P100 filters is a requirement. Try not to use power tools like drills, Dremels, sanders, etc.; perform everything by hand using wet methods. In addition, you aren't allowed to eat, smoke, drink, or chew gum while working. When finished for the day, perform a complete wet wipedown of your work area , and dispose of any used cloths in the trash. Oh, yeah, keep the wife and children away from what you're doing....
Lastly, repainting will encapsulate any lead present, so a complete lead paint removal will probably not be necessary.
Sorry for rambling. I was writing as thoughts entered this old brain. There's probably more I could tell you; if you have any specific questions I can help you with, please don't hesitate to e-mail me. Working with lead can be tough, but the consequences of not following some work process standards can be tougher.
All the best,
Gip Winecoff