I pondered this too for a nanosecond before I posted earlier. From a reader:

In your post regarding the campaign contributions of reporters, you used the
phrase “wet your whistle.” Some people seem to prefer “whet your whistle.”
Stupid little things like this shouldn’t bother me, but since I have no
life, they do. Is either whet or wet acceptable?

A very, very, quick Google search seems to confirm my suspicion. You wet your whistle — as in at a bar — but you whet your appetite.