Update OS X recovery USB stick with Mavericks

I've got a Snow Leopard 8GB USB stick that I got from my MacBook Air. Now that Mavericks is available, I'd like to update that USB stick with Mavericks.

I can't seem to be able to format that disk:

$ diskutil list
/dev/disk1
   #:                       TYPE NAME                    SIZE       IDENTIFIER
   0:     Apple_partition_scheme                        *8.1 GB     disk1
   1:        Apple_partition_map                         30.7 KB    disk1s1
   2:         Apple_Driver_ATAPI                         2.0 KB     disk1s2
   3:                  Apple_HFS Mac OS X Install        7.7 GB     disk1s3

I've tried the Disk Utility, it recognises the USB stick as an optical disk, and it refuses to erase it (I guess because my MacBook Air doesn't have an optical drive).

I've tried the following:

$ sudo fdisk -i /dev/disk1
fdisk: could not open MBR file /usr/standalone/i386/boot0: No such file or directory

    -----------------------------------------------------
    ------ ATTENTION - UPDATING MASTER BOOT RECORD ------
    -----------------------------------------------------

Do you wish to write new MBR and partition table? [n] y
fdisk: /dev/disk1: Permission denied
$ sudo dd if=/dev/zero of=/dev/disk1
dd: /dev/disk1: Permission denied
$ sudo diskutil eraseDisk jhfs+ newdisk /dev/disk1
Started erase on disk1
Unmounting disk
Error: -69877: Couldn't open device

What else can I do? I'd like to erase it and format it as HFS+ (journaled).