It's been a while for me and I never did watch all of them, but no, I think Sherlock is a whodunnit, heavy on the drama, plus the twist of some narration from Watson's blog.
The first episode opens with several people seemingly taking a pill to commit suicide. But someone is making them do it somehow. We don't know who, we don't know why. Who did it? Whodunnit genre.
Where if it were a Howcatchem genre, the identity of the baddie is revealed up front and the episode is about how the detective figures it out and nails them. How did the detective catch them? Howcatchem.
Monk, if you ever saw that one, would sometimes do whodunnit episodes and sometimes howcatchem episodes.
Yeah, I would call that a "killer of the week" format. There is a new crime/murder every week. Sometimes there is a season-long story as well (Natasha Lyonne's character running away from the Vegas baddies) and sometimes it's just the killer of the week story. Murder, She Wrote is a good example of the latter; you can watch MSW episodes in pretty much any order, it doesn't matter because each episode is basically self-contained. Any story external to the killer of the week is just to service actors being replaced or setting Jessica Fletcher in different locations beyond her hometown so she can face a new killer of the week. MSW is a whodunnit and also a killer-of-the-week show.