Hi @MattH_Work
Regardless of adding to the menu or not, I think you would use the same methods illustrated in the example addins I posted, to interact with the OnSelectEvent to determine what has been clicked on, in combination with the OnLinearMarkingMenu event and/or the OnRadialMarkingMenu event to get the command controls of those menus.
So to right click on a feature in the browser and get the contents of the linear marking menu, I would do something like this:
Private Sub Events_OnLinearMarkingMenu(ByVal SelectedEntities As Inventor.ObjectsEnumerator,
ByVal SelectionDevice As Inventor.SelectionDeviceEnum,
ByVal LinearMenu As CommandControls,
ByVal AdditionalInfo As Inventor.NameValueMap)
Dim sMsg As String = Nothing
For Each oControl As CommandControl In LinearMenu
sMsg = oControl.DisplayName & vbLf & sMsg
Next
MsgBox(sMsg)
End Sub
which when right clicking on an Extrude feature, would result in something like this:

However, the "my browser" part of your statement throws me a bit.
Are you building a custom browser?
If so, is the right click context menu empty by default when you click on a feature in that custom browser?
I hope this helps.
Best of luck to you in all of your Inventor pursuits,
Curtis
http://inventortrenches.blogspot.com