(I Googled and found a fare few people wanting this with none of the methods working completly. So did a bit of research.)
Normally if you use Google Chrome Portable then make "Google Chrome" the default browser app via "Windows Settings" it opens the normal Chrome (the one in C:\Path\PortableApps.com\PortableApps\GoogleChromePortable\App\Chrome-bin\chrome.exe) and uses the profile in \Users\user_name\AppData\Local\Google\Chrome.
Even if you associate everything web related (HTML, SHTML etc.) to the Google Chrome Portable executable in some cases (like when an application opens a URL) it will use the normal, non-portable chrome.exe that's also created during a Google Chrome Portable install.
This is because Windows uses a "Application User Model ID" to allocate certain behaviours.
These instructions simply points the registry's Application User Model ID entry for Chrome towards the portable executable (instead of the "normal" one.)
1.) Click on the start button and type "regedit" , click on the regedit icon.
2.) Got to:
(Where the portion that says "NUMBERSANDLETTERS" will be a unique string of numbers and letters.)
3.) Create a backup by clicking File > Export
4.) Change the value in:
to "Google Chrome Portable"
5.) In the following registry keys change the value (double click on them.) Change the path from the normal (non-portable) chrome.exe to the GoogleChromePortable.exe path. Make sure to only change the paths and leave other portions unchanged.
Now when you go into Windows settings and select a default browser you will have a "Google Chrome Portable" option and all links will open using the portable version.