I think that Cookie Clicker should have its own PortableApp because you cannot download it from anywhere. This would be a very popular game app!!!
New: Kanri (Oct 9, '24), Platform 29.5.3 (Jun 27, '24)
1,100+ portable packages, 1.1 billion downloads
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As of right now, Cookie Clicker is online only so it's impossible to make it into a portable application. If a standalone version was made, it might be possible, but it is still not a guarantee.
If you wish to save and continue your progress from one computer to another, then why not just use a portable browser.
Since your progress is most likely saved through browser cookies (ironically), then it should transfer just fine.
If at first you do not succeed, use more sticky tape.
It might be saved with Flash cookies, which are not portable with your portable browser.
Sometimes, the impossible can become possible, if you're awesome!