I want to run Spotify searches from within a Spotify app (to find tracks for an artist, for which I do not have a Spotify URI, only the name).
I have not found func
This is not the finest way to solve your problem. There is a direct API for searching within your app. See Juan's solution.
But you could also talk to ws.spotify.com directly when you add the domain to your app's manifest.json.
"RequiredPermissions": ["http://ws.spotify.com" ]
e.g. http://ws.spotify.com/search/1/track.json?q=kaizers+orchestra, see their Developer Site. The response contains the header "Access-Control-Allow-Origin: *", so you should be able to query from within your app.