Re: 223/5.56 pressure vs handgun pressure What's close
If clearances were not an issue and it was purely a stopgap/functional issue, it could be done.
You can get a pretty short suppressor for your 5.56 but it is really apples and oranges. Delta P Design makes one that is less than 4" in length and would physically fit, but it still would not be something I would recommend.
A good 22LR suppressor will be substantially lighter and more important, will be small enough in diameter that you can likely use your sights. In addition, most 22LR suppressors are inexpensive enough that it is worth considering a dedicated 22LR suppressor. Another consideration, depending on the 22LR conversion used, is if the 5.56 suppressor will clear the guide rod on your particular pistol.
When getting into suppressors it is common to want to use a one size fits all approach. Thinking of a suppressor in the same terms as an optic makes sense. You could use a 4X optic on a rail mount for all of your firearms using optics. In practice it is really not a good fit for all uses and it would rapidly be apparent that there were better options based on the application.
HTH. Best of luck with your project.