I think you should rephrase your question.
The main issue is not which part of the chain is noisiest.
Have you ran the Shure mics directly into the R-09 until now? Are they supposed to be ran on plugin power? And if so, did you experience that the signal was hot enough?
Or did you have to crank up a lot of gain with the R-09? In that case, you would surely benefit from an external pre!