Boy, you really don't want to do a Delete, do you?
Actually i think i understand now a bit more about why he doesnt want to make a delete, because Archive serves no purpose other than to record a log of items.
So when you "archive" something you are really just deleting it (and putting it into the log (archive)).
I think the term archive made me think we could bring back timers from the archive, like if we created a 10 minute egg alarm, and then archived it, we could recreate it from the archive easily. In other words i thought the archive was more like a template.
If you keep functionality the way it is now, maybe i would suggest changing "archive" to "log".
And in the log put a note next to each alarm about whether it was [CANCELED].
And then i still say change from A) Archive to C) cancel.
(in other words you dont need to create a new delete function, you just have to rename the Archive function to Delete or Cancel, since it serves the same purpose).