I love the idea, but international postage is fraught with risks. I run an e-commerce business, and I've been involved with logistics one way or another for most of my working life.
Many countries will have an internal post service which allows bullion postage (here in the UK, Royal Mail Special Delivery will do it, if it's correctly declared and insured). Fedex, DHL, UPS and most other couriers specifically state that they won't carry precious metals internationally.
Assuming you can find a courier willing to ship and insure it, you'll have to get the paperwork spot-on, and there may be import duties and customs fees that need to be paid. It is possible that might put the price up to an unfeasible degree.
What you might want to investigate is reputable online gold dealers in each country, to see if they'll accept a payment from abroad with a delivery address (possibly stated as a gift address) in their country. That way, winners still get a prize in real metal, but with lower shipping costs and at far lower risk.
Thanks for the thoughtful comment!
Using local (to the winner) dealers as distributers is another idea to put in the mix definitely.
Though it does make the prizes less personal. Members usually like to hand pick pieces from their stack.
Also I think many members deliberately mis-label packages as medallions or collectibles to get around bullion postage restrictions, but to be fair - it usually isn't just bullion and they ARE collectible. If we try to do it "By the book" the MR probably also dies conceptually.
Really appreciate your suggestions and info.