How to resize a camera's orthoSize for an object to fit inside its rect viewport?

Hello, this is another follow-up of this series of questions. So I'm still working on the Examine feature of Resident Evil.

Short summary of my setup once again:

1. I'm using NGUI, I have a "Examine_UI" UI, which has its main camera (which you can see in the left image below). This camera can only see the UI layer, which is "2D_Examine"

2. Going down you got "ExamineCamera" which only sees the "ExamineArea" (grey window in the middle of the UI, left image) and its children.

So after I got the weapon to appear only in the desired area, and re-calculating the examine camera viewport every time the examine window changes position, I'm stuck with a problem:

Weapons/objects could have different scales upon examining them, which means, they could either appear big in the examine window (large scale) or small. What I would like, is to have the weapon fit nicely inside the examine window no matter how big or small it was.

I can think of 2 ways of achieving this:

1. If the gun was bigger/smaller, I would keep increasing/decreasing the size of my orthographic camera, till the gun fits. The problem is I don't know what 'till the gun fits' means! I mean what would that imply? To answer, I'd have to find a connection between: The gun's size and/or scale, the camera's orthoSize and its rect viewport. What is the connection between those?

2. Instead of changing the camera's size, I could maybe scale down the gun till it fits. Here, I think I might be able to figure out what 'till it fits' means. I could maybe take the bounds of the gun's boxCollider, and compare it with the camera's rect viewport, keep scaling down, till they're about the same width and height. However that requires me to save the gun's previous scale, so that after I'm done examining I take it back to that scale.

I would really like to apply the first method, it sounds more efficient and faster, and don't mess with the scale at all.

So, how can I achieve it? change the cam's orthoSize till the gun fits the window? Is this possible or am I gonna have to go with the 2nd method, which I'm also having trouble with :/ - I just want ideas, thoughts, not code.

Please notice that I only want to do this thing upon the beginning of examining an item.

If you're interested in my current code of examining:

 public void ExamineItem(Item item)
 {
     // if it's the same item, don't do anything
     if (item.gameObject == examineInfo.itemObj)
         return;

     // if there's already an item we're examining, let it go
     if (!doneExamining)
         Notify_DoneExaminingItem();

     doneExamining = false;

     // activiting the item object if its disabled
     examineInfo.wasActive = item.gameObject.active;
     if(!examineInfo.wasActive)
         item.gameObject.SetActive(true);

     // store item's layer and parent, to get back to it when we're done examining
     examineInfo.previousLayer = item.gameObject.layer;
     examineInfo.previousParent = item.transform.parent;
     
     // change item layer to the examine pivot point layer
     MiscOps.ChangeObjectLayer(item.gameObject, examinePivot.gameObject.layer);

     // adding it as a child to our examine pivot
     item.transform.parent = examinePivot.transform;
     examineInfo.itemObj = item.gameObject;

     // zeroing out its local pos and resettins the scale
     examineInfo.itemObj.transform.localPosition = Vector3.zero;

     // nuke gravity, if any
     examineInfo.rigid = examineInfo.itemObj.rigidbody;
     if (examineInfo.rigid != null)
         examineInfo.rigid.useGravity = false;

     // set strings
     examineStrings = item.examineStrings;
     currentStringIndex = 0;
     UpdateText();

     // finally show the examine window
     Show = true;
     examineArea.examineCamera.RefreshCamera();
 }

 public void Notify_DoneExaminingItem()
 {
     Show = false;

     if (examineInfo.itemObj == null)
         return;

     // if it was active, activiate it
     if (examineInfo.wasActive)
         examineInfo.itemObj.SetActive(true);

     // get its previous layer back
     MiscOps.ChangeObjectLayer(examineInfo.itemObj, examineInfo.previousLayer);
     
     // if it has a rigid body, get its gravity back
     if (examineInfo.rigid != null)
         examineInfo.rigid.useGravity = true;

     // free it, get its parent back
     examineInfo.itemObj.transform.parent = examineInfo.previousParent;

     // done
     examineInfo.itemObj = null;
     doneExamining = true;
 }

 public bool Show
 {
     get { return show; }
     set 
     { 
         show = value;
         examineGuiRoot.SetActive(show);
     }
 }

 public class ItemToExamineInfo
 {
     public GameObject itemObj;
     public Rigidbody rigid;
     public bool wasActive;
     public int previousLayer;
     public Transform previousParent;
 }

Thanks all. I hope this is the last problem in this series.