Never put anything valuable in stowed baggage. However, in a carryon that stays with you is fine.
You can and might get different opinions as to the reliability of the various delivery services as well as insurance options.
Your choice might be influenced by the value of the jewelry.
In my life, all the valuable jewelry I have wouldn't take up any considerable amount of room in my carryon.
I would prefer to carry it with me, but, if not, would use USPS.
This conversation may help you decide.
How to ship rare coins and precious metals safely [Archive] - EcommerceBytes Discussion Boards