[syslinux] Boot USB:SATA:Partition4 from USBstik?

[eas lab]

I want to be able to make a USBbootStik for my laptop, as I repeatedly
did for the now stolen PC.
I've got a copy of the required 2009, Slackware13 partition, saved to a
USBdisk. And I've located the 175-line: <make bootStik script> .
  Of course just "chroot"ing Slak13, won't allow <make bootStik>.
But why can't someone here, provide the info to make an equivalent
bootStick from StikBooted TinyCore64 which already
uses: /boot/isolinux isolinux.bin  isolinux.cfg ..etc.
Even better would be if the TC64 stikBooter could be extended to boot
the Slak13 partition of the USB installed/chroot-able Slak13.

  Some of the key-lines of the SlakScript are:--------------------
    chroot $T_PX /sbin/mkdosfs -I -n USBSLACK -F 12 /dev/$STICK
$DOSSIZE 1> /dev/null 2> /dev/null
  fi
  if [ ! -d $TMP/bootdisk ]; then
    mkdir $TMP/bootdisk
  fi
  mount -t vfat /dev/$STICK $TMP/bootdisk 1> /dev/null 2> /dev/null
  if [ -r $T_PX/vmlinuz ]; then
    cp $T_PX/vmlinuz  $TMP/bootdisk/vmlinuz
  elif [ -r $T_PX/boot/vmlinuz ]; then
    cp $T_PX/boot/vmlinuz  $TMP/bootdisk/vmlinuz
  fi
  # We don't need the isolinux bootloader with syslinux do we?
  #cp $T_PX/usr/share/syslinux/isolinux.bin $TMP/bootdisk/
-------------------
  umount /dev/$STICK
  rm -r $TMP/bootdisk
  # Make the device bootable:
  syslinux -s /dev/$STICK 1> /dev/null 2> /dev/null
-------------------
Please advise.
==TIA.