Sorry if this is obvious and old-hat but although this service has existed for many years I wasn't aware of it (or had forgotten about it) until recently. I am passing it on as it may help others looking to protect their privacy.
Until recently I had a very small number of discreetly named punting related bookmarks buried deep within my Google Chrome bookmarks, but my other half was now going to be making more use of the shared PC for a while since she needed software that was only installed on there. My main concern was that when you type a URL in the Chrome web browser, even by typing just one letter it uses your saved bookmarks to autocomplete. As long as you browsed previously in Incognito mode it won't use your private search history, but it will use any bookmarks on the default Chrome browser account.
So I looked around for a way to save bookmarks outside of the browser and this fits the bill.
If you use Gmail for your punting mail then opening an Incognito tab and logging into Gmail logs you into "Google" for that Gmail account. Otherwise you need to log into Google using your punting email address. That will mean that Google is tracking your browsing of course (in theory you can amend settings to avoid that) but if you were logged into Gmail it would have been doing the same anyway.
Now you can go to
External Link/Members Only and you can save any bookmarks there.
You would just need that one "safe" bookmark in your browser bookmarks - to
External Link/Members Only - to get all your saved bookmarks without any local PC storage or autocomplete risk. There are user defined categories available to manage the list.
You can add bookmarks manually, of course, but you can also add a toolbar button that will add the currently open page to your Google Bookmarks list. At the bottom of the Google Bookmarks you'll see: "Bookmark pages more easily. Drag this bookmarklet to the Bookmarks bar of your browser:".
Closing Incognito windows then logs out of everything without a trace.