Okay, that is a little different then... :)
Then you mean a residential type handrail I assume? You don't need to use standard handrail mounting brackets - there is an alternative method. Do you need a handrail on both sides?
You should secure it into a stud. Do you have any idea where studs are behind the wall finish? The wall finish would most likely be luan which is a thin form of plywood. Yes, no drywall. Not very strong and it will only be secured in place by thin gauge staples. I would avoid the exterior wall if possible unless you know 100% certain there are studs in the wall cavity and exactly where they are. If a fiberglass exterior, there may not be studs anywhere near where you want.
If you have an intersecting partition wall behind the stairway wall or a bathroom door at the top of the stairs, you should find a studs there. You may need to get creative to get something to work and be secure enough. What do the numbers mean? Height above the stair or floor?
Have you go a link to a floorplan and photos? That might help in giving suggestions. There should be some things you can do to strengthen the wall depending on what is in your FW.