Actually, I missed the point of your question. You want Skype installed on the USB from the get-go. My other answer pertains to installing Skype after Ubuntu installation to a hard drive.

Really, the only way to go about doing what you asked is to either remaster the filesystem.squashfs or install it into casper-rw. But, either will require being in a Linux system (even the LiveCD, but will require several gigs of RAM to work with). You might be able to do it in Cygwin, but it will require knowledge of how to acquire and install Ubuntu source code.

Creating a casper-rw is the same as intalling it after booting the Live USB with persistance, but that's not what you want.

If you're looking to have it installed in the main filesystem, here's what you'll need to do:

sudo unsquashfs /cdrom/casper/filesystem.squashfs

sudo mount --bind /dev squashfs-root

sudo mount -t proc none squashfs-root/proc

sudo mount -t sysfs none squashfs-root/sys

sudo mount -t devpts none squashfs-root/dev/pts

sudo cp /etc/resolv.conf squashfs-root/etc

sudo chroot squashfs-root

# export HOME=/root

# export LC_ALL=C

# dbus-uuidgen > /var/lib/dbus/machine-id

# dkpg-divert --local --rename --add /sbin/initctl

# ln -s /bin/true /sbin/initctl

# wget http://download.skype.com/linux/skype-ubuntu_2.2.0.35-1_i386.deb

# dpkg -i skype-ubuntu_2.2.0.35-1_i386.deb

# rm skype-ubuntu_2.2.0.35-1_i386.deb

or

# wget http://download.skype.com/linux/skype-ubuntu_2.2.0.35-1_amd64.deb

# dpkg -i skype-ubuntu_2.2.0.35-1_amd64.deb

# rm skype-ubuntu_2.2.0.35-1_i386.deb

# rm /etc/resolv.conf

# rm /var/lib/dbus/machine-id

# rm /sbin/initctl

# dpkg-divert --rename --remove /sbin/initctl

# exit

sudo umount squashfs-root/dev/pts

sudo umount squashfs-root/dev

sudo umount squashfs-root/proc

sudo umount squashfs-root/sys

sudo mksquashfs squashfs-root /cdrom/caser/filesystem.squashfs

All the above are if you're running from the LiveUSB, the only difference from Cygwin is the paths to your USB (referred to as /cdrom from the LiveUSB). Also, you'll have to compile squashfs-tools from inside cygwin. The source can be downloaded from packages.ubuntu.com/oneiric/squashfs-tools.

All-in-all, as you can see it's much easier to just install it once running the LiveUSB (if you stalled with a persistence file, you'll only have to install it once and you're set). If you want help on how to make a persistence file, I can show you that as well.