Not all hand drills have a retaining screw.
Retaining screws are usually common on older USA made drills, and are still common on some drills made by US companies, but the screws aren't always standard. The screw head type can also vary if the drill has a retaining screw. I've seen hex head screws, slot head screws, and phillips screws, used to retain different drill chucks, or included with replacement chucks.
Also, not all drills or drill chucks are manufactured to use a retaining screw. In Europe it seems more common that drills do not use a retaining screw. I've seen drills from Fein, Metabo, and AEG that didn't use a retaining screw, even when the drills were reversible. When the drills don't use a retaining screw, the drill chuch is usually secured with threadlocker on the threaded shaft. In this case you would hsve to tighten the chuck in a vise, and run the drill in reverse on low gear, to remove the chuck, or tighten a large hex key in the chuck, and tighten the hex key in a vise, to unscrew the chuck. Be carefull not to break your wrist in the process.
Some drills, particularly European made ones may also use a tapered shaft rather than a threaded shaft. I'm not sure how common this is, but some Fein drills are still manufactured with a tapered spindle, and I know some older UK made Black & Decker drills were manufactured with tapered shafts as well.
Some of the Dewalt XRP drills originally came with a German made Rohm Supra type chuck that were not designed or made with a thru hole for a retaining screw. These drills had the chuck bonded on with dome type of threadlocker. I'mnot sure how the hammer and hex key method works to remove these chucks. You may have to use the vise method.
on the harmonious outcome.