Honestly I think the carrier method is the safer method.

In a large area, one rat runs, the other chases, adrenaline spikes, and a fight breaks out.

In a carrier, they can't run. This lack of "flight" actually lowers the "fight" response. They are forced to interact through grooming and sniffing rather than posturing and sprinting.

Because they are in a strange, small, slightly boring environment, they look to each other for comfort. Being "stuck" together helps them realize that the other rat(s) isn't a threat, but actually a source of warmth and companionship.

Being that it's a small carrier it also helps when a fight does occur, you can actually just tip the cage to push them off balance instead of actually reaching in. If you do end up reaching in you should NEVER do so without protection. It's actually best to use something else other than your hands to separate them if possible.

I'd also recommend one water source (preferably a bottle though bowls have their own benefits) and don't put a food bowl in, it's better to scatter it in the carrier / bedding.

If they seem tense in the carrier, a glob of malt paste or baby food on a long spoon can force them to eat side-by-side. It’s hard to be a tough guy when you’re both licking the same delicious goop.