I'm still unable to delete the actual source files from the shapefile directory, but deleting the featuretype took care of all WMS and WFS artifacts. For any future searchers who stumble across this question, here's the proper REST url for this sort of request.
DELETE http://myserver:myport/geoserver/rest/workspaces/workspace/datastores/datastore/featuretypes/typename?recurse=true
Make sure not to include the workspace before the typename ala "workspace:typename".
If I ever figure out how to make geoserver remove the actual files from the folder I'll update the answer.