What would be the best approach for achieving this?
I would rather do this on the face of the drawer rather than tacking beading on to a recess on the drawer front if possible.
This is not a job for the router, at least not in the way you're thinking. Here are two quick guides to how this is generally done:
Two Ways to Make Cock Beading on Fine Woodworking.
Q & A: Cock-Beading on Drawer Fronts on Popular Woodworking.
You're hoping to form this in situ on a solid wood drawer front, I suppose it's possible with a tricky operation using a router and the right bit, but the corners might be still end up less precise than you'd like and I think it would be more straightforward (and surprisingly, not slower) to do it using hand tools.
The best option IMO would be using a scratch stock, since you don't need to buy anything. You can make one for yourself in under half an hour using stuff you probably already have in the shop (a scrap of wood or plywood, even MDF would do in a pinch) a few screws and a small piece of steel*.
Here's are a few basic scratch stocks:
Scratch stocks, like all scraping tools, can be pushed or pulled, sometimes used in both ways on the same job, according to how the wood grain lies as well as the preference of the user.
Note; scratch stocks are generally used to create grooves and other details that run the whole length of the stock being worked (through grooves). In order to form accurate, repeatable stopped grooves I think you'll want to use wooden stops at both ends, very firmly clamped or temporarily tacked to the bench with small brads. And needless to say some practice is advisable before committing to scratching the detail into your drawer fronts!
*Usual candidates for the blade for a scratch stock are short lengths of broken bandsaw or hacksaw blade, or a piece of card scraper or saw plate which are much the same steel usually. But even a piece of stainless from a cheap kitchen knife will do the job quite well, particularly if a magnet will stick to the blade (non-magnetic stainless would still work but would blunt a lot quicker).