For the record: It is NOT allowed to use spotify in any public function without express written permission. So we can’t help you on that end.
Secondly, at the core of DJ-ing is the most important skill of all”: “knowing what must come next”. Something that can only be learned by DJ-ing out in front of an audience. For that reason it is not really possible to prepare a playlist in advance. What you can do is create mini-playlists of 3-4 tracks that go together which you then use as building blocks for your live set, taking away some of the stress of having to think about every next track.
While I haven’t tried the setup you are describing, I am guessing this will work. While the transmitter might fit into the headphone jack, that is not the place to hook it up. It should be hooked up to the master output of the controller. The headphone jack should have (duh) a headphone attached so that you can pre-listen (cue) the next track. In silent disco you will actually do all of your mixing in your headphones as you can’t hear what the audience is hearing from monitor speakers or anything.
Hope that helps some.