I would dd the whole thing to disk, once you know the block size. cpio is not going to be variable block sized, so it should dd fine.
Unfortunately with cpio, I believe it is just "header" followed by data with buffer, then another header, etc.
So if the tape ended prematurely, you might not know it.
Now what is nice, you can extract the data even if you
have only tape of a multiple tape, since you can seek to the next good header and it looks like a cpio image.
For this exact reason, when I used to make corporate images I would make the first file an info file that contained a listing and extraction method in some simple format (tar) followed by the actual tape file.