I guess I could just re-compute the checksum and match the value with the value from the file. But is there a less boilerplate way to do this in Java?
No, you have to re-compute the checksum and compare. There's no other way of doing it
You can reduce boiler-plate by writing a method to do your SHA-1 hashing. Then it's just a one-line method call to produce the checksum and verify it.