I've shipped literally hundreds of bows all over the world--pretty sure I've never shipped one in PVC.
PVC does come in larger sizes than 4". If you have a neighborhood hardware store, or know someone at your local water dept, you may be able to get a short section without having to buy the whole stick. Shipping cost is going to be a bugger, on top of buying caps.
Whichever way you ship, I'd pad the ends very well (newpaper works just fine, or bubble wrap, or foam shipping wrap). I'd also pad the riser well, and if any points on the limb contact the tube or box pad them too. I use mostly newspaper. If you have enough space in the container for the bow to shift around, fill it in with packing material (newpaper, bubble wrap, foam peanuts, etc.)
This has worked for me for years, shipping all over the world in cardboard boxes. I've had some boxes that looked rough when they arrived, but never had a bow get damaged. I always insure them just in case--the insurance sticker on the box might be the difference in how it gets treated.