Yes, you can do it. Actually, it is done routinely. But it may depend on what you actually have. The .300 Win mag has been chambered in both CZ 550 "American" (standard length action) and "Safari" (magnum length action). The .404 is short enough that it will technically work in either, but there is a lot more room for overall cartridge length variations and magazine capacity with the magnum action...
A rebarrel job with an identical CZ barrel profile including integral rear sight boss and under-barrel recoil lug + barrel band front swivel + barrel band front sight + opening the bolt face + tuning up the extractor shape and tension on the new cartridge + tuning up the feeding rails for the new cartridge should run you anywhere around $1,000 to $1,200. Dwayne at American Hunting Rifle (AHR) or Meagan at Triple River Gunsmithing can do this for you easily.
While you are at it I would suggest you ask either Dwayne or Meagan to install a bolt-mounted, firing pin-blocking safety (a.k.a. "Winchester 70-type 3 positions safety") + replace the set trigger with a direct AHR or Timney trigger + fill and straighten the bolt handle. This will cost another $900.
I would also suggest that you drop the barreled action in a Bell & Carlson kevlar stock with full length aluminum bedding block and bedding pillars. This is another $300, but that stock will never crack or warp on you.
The net outcome will be a near perfect DG rifle.
The other way to think about this
Fastrig, could be to keep your CZ 550 .300 as the penultimate PG rifle, buy a used-as-new $950 CZ 550 magnum on Gunbroker.com in whatever caliber (typically .375 or .458) and have it rebarreled. You would then have a near perfect PG / DG African battery.
