The box does seem somewhat large for 20 coins in flips. Of course it does leave you plenty of room for padding between flips.
Registered with proper declared value is the safest way to ship them. It is slower, but safe and over about $1K in declared value it is also cheaper than other methods. Registered can also be protected for higher values. Up to $25K. Other USPS methods only go up to $5K and carriers like UPS or FedEx max out at $1K.