From further research on my part, it appears that SQUASHFS is not a part of the Linux kernel that I am running on Ubuntu, which now uses 2.6.27-14-generic
Therefore, it would appear that I am out of luck with wanting to experiment with Tinycore at this time,
unless I wanted to go through the hassle of compiling a new kernel which contains SQUASHFS.
That is something that I have not attempted and perhaps requires a little more skill than I have.