If I understand correctly, you can convert one file with
./convert /path/to/file >/path/to/file.new
mv /path/to/file.new /path/to/file
To apply a command to every file in a directory tree, use the `find` utility. Since you need to execute a complex command for each file, you need to invoke a shell explicitly.
find /path/to/top/directory -type f -exec sh -c '
/path/to/convert "$0" >"$0.new" &&
mv "$0.new" "$0"
' {} \;