Memoir '44 and other games under the same system (there's an Ancient Rome themed one, for instance) are fairly accessible and (depending on scenario) play quite a bit faster than most Risk games. They're (mainly) 2-player, though. They're also at the battlefield level, rather than worldwide strategy or anything like that.

Diplomacy's either a much better or much worse alternative to Risk. Depends who you ask. Not directly comparable but scratches the same itch, possibly better (see: depends who you ask).

The Board Game Geek site probably has some lists for semi-casual or otherwise less-hardcore wargames. That'd be the place to look. Then see whether Shut Up & Sit Down has done a video review of any that look interesting to you, before buying (they have for Memoir '44, IIRC).