As someone who works in the museum field, I can tell you that most curators are willing to assist visitors with legitimate and reasonable requests, especially when it comes to research. After all, that's part of their job, and military museum curators are aware that many scale modelers rely on them for information.
However, you'll have better luck if you follow certain protocols. First, contact the curator well ahead of when you plan visit. Most museum staff loath drop-ins, which always seem to come just when you're rushing to a meeting with the board of directors or frantically trying to complete your quarterly budget before day's end. Try sending an e-mail, or even better, send a letter by snail mail. Explain just exactly what is is you want to take a look at and why. Specify a time frame that leaves some flexibility for the staff. Ask about museum policies on photography, handling, or in this case, climbling on, exhibits.
Chances are if you use this approach, someone will be willing to accomodate your request. But don't take it too hard if you get a flat refusal. Most museums are operating with reduced staff these days and can't spare anyone for anything beyond the bare basics.
Good luck
seventrs