When I shipped my ammo I personally used UPS.
"UPS accepts for transportation such ammunition as constitutes "cartridges, small arms," as defined in 49 C.F.R. § 173.59. All other allowable ammunition shipments are accepted only on a contractual basis, and must be prepared under the rules for a fully regulated hazardous material.
Ammunition will be transported only when packaged and labeled in compliance with 49 C.F.R. § 172 (Hazardous Materials), and must be shipped in accordance with the UPS Guide for Shipping Ground and Air Hazardous Materials. To meet the exception for Limited Quantity, ammunition can be shipped via UPS Ground only within the 48 contiguous United States, UPS Ground Intra-Oahu and Intra-Alaska.
To qualify as Cartridges, small arms "Limited Quantity", ammunition must be:
Ammunition that does not exceed 12.7 mm (50 caliber or 0.5 inch) for rifle or pistol cartridges or 8 gauge for shotgun shells; or
Ammunition with inert projectiles or blank ammunition"
some info from UPS website.
However some parts that are not ammo, but the once I needed for hunting I purchased many times from aliexpress. I use extension for that (to control the prices on the products and to track the parcel. They also have a nice blog with useful info like this article https://alitools.io/en/blog/can-you-use-paypal-on-aliexpress/.
