Can I charge shipping as a percentage of the order value?

Yes, with the Shipping Zone plugin:

1. Go to Plugins → Shipping Zone and click Edit on the zone (or + Add Zone to create one).
2. Under Shipping methods, click + Add method.
3. Set Type to Percentage of cart and enter the rate in Percentage of cart (%), for example 5.
4. Give it a Label customers will see.
5. Optionally fill in Free above cart total.
6. Click Save zone.

Wcart then charges that percentage of the cart total for addresses in the zone.