Most folks overthink swaging jacketed bullets down to a smaller diameter.
It's possible to swage .224 diameter bullets to .204, but "why" when bullets are available?
If you decide to do this OP, you will need to size down in "increments." Doing it all in one pass, especially on such small bullets, will likely lead to a lot of lost projectiles.
I have swaged .323 bullets, down to .318 diameter for some older Mausers, and I can get away with doing it with one pass through a die.
First, you need to get a machinist to make up a set of dies with a taper bore over an inch, leading to a straight bore appx 3/4 inch long that will reduce the diameter by appx .005 with each pass.
The last swaging die will need to be a bit tighter in the straight bore, by a couple of thousandths, as the jacket/core of the bullet will have some elasticity, and will swell a bit after being swaged.
I had to push the bullet through the last die 3-4 times before it slipped through easily, and the diameter was where I wanted it to be.
The bullets need to be lubed with a good high pressure grease before they are pushed through the swaging die.
The bullets will also have to be cleaned after the swaging process, before being loaded into a cartridge.
Believe me, you don't want to do this unless there isn't any other way to acquire proper factory projectiles.
If you've got a bunch of 22 cal projectiles, you're much better off selling them, even if it's at a loss, and purchasing factory projectiles in .204 diameter.
I get it, selling .224 diameter bullets, especially in quantity, has become difficult, with the ban of semi auto rifles chambered for 223rem.