You need to research the laws at your point of entry.
Leaving here is not an issue.
I have had clients take meat from NZ to the USA.
one of two ways.
-We drop the meat the a butcher and it is processed and packed then shipped
-we drop the meat to a butcher and it is processed and packed and they take it with them frozen on the plane.
Meat is supposed to be processed and packed at a proper facility.
The main issue here is the time window for a hunt, and the cost. shipping meat international makes little sense.
There is a very good reason most countries do not want meat coming across borders, CWD, foot and mouth, TB etc etc can cost out economies billions and also put peoples lives at risk.