Title fairly well summarizes the question - I really enjoy Beethoven's 9th, esp. the 4th movement, and would really like to hear the orchestration without the chorus. I've tried some amount of Google-fu but have been unsuccessful in identifying if there are any recordings of just the orchestration (which has some beautiful oboe and clarinet lines) without the vocals.
There is one in your future. You could visit a rehearsal with the orchestra before they bring in the choir. This may be the only way to get a recording. Neat question that is for sure. Beethoven's ninth is so full of intriguing passages. You may need to massage some connections with powerful music personalities in your locality.
One idea is, to try a recording of the piano transcription by Liszt, e. g. with Scherbakov. Definitely no chorus there. Of course it has to be checked, whether your woodwind solos are recognizable here, but I found my brain to supply from memory some tone colors the piano was unable to provide.