Not sure I follow how the type of gun and ammunition you will be using comes into play. When I ask permission to hunt, it goes something like, "Hi, would you mind if I were to hunt <game species> on your land?..."
The type of firearm and ammunition I might use is my methods and means and has never been inquired. For example if I secure permission to hunt doves on a farm, I own several guns I might chose to use on any given day. Whether I show up with my 12 gauge pump, 20 gauge SXS, or flintlock fowler is my prerogative and has no bearing on my permission to hunt there.
Now around here there are land owners who might give you permission to hunt deer during archery season, but not rifle, or vise-versa. But even then, if I am granted permission to hunt say archery, then whether I show up with a compound bow or a traditional long bow is of no consequence to the landowner.