There are certainly many solutions how to do this off-site. (Some were suggested in the comments.)
I will also point out that you could post a question and immediately delete it. You still can see it if you keep the link.
Some things to keep in mind:
- Many deleted questions can lead to question ban.
- You can no longer edit the question while it is deleted. (But you can edit an answer, if you post one too.)
- If you favorite the question so that you can find it more easily, other 10k+ users can see the question if they look at your favorites. (And also if the question appears on some other list of questions, 10k+ users can still see it. However, from the top of my head I cannot think of another list where the question is likely to appear.
- 10k+ users can view deleted question if they have link to it. So theoretically it might still be visible to some other users. (If they notice the question during the short period while it is not deleted or if they have the link from somewhere.)
Related question: Would using deleted (“hidden”) questions on math.SE for personal use be considered misuse of the site?
Still, I think using some tool to store the question elsewhere is better. The only advantage of this approach that I can see that you have question (possibly with some answers) available directly here on the site. (This is definitely not ideal, but it is the ony possibility how to do this within the site if you want the post to be accessible mainly to you.)