I did exactly that with my JTV 59, put on 009 Elixirs. At the same time I adjusted the action to make it a bit lower. No issues at all, although I did (of course) check and adjust the intonation. It played great after. No adverse issues with the 009's at all.
I wasn't sure about resonance and whether it might be compromised. I thought it might lower the actionslightly too as there would be less stress on the neck. My intonation was way out on first play and I even had to move the tailpiece backwards on the low E side due to lack of adjustment. I think I will go ahead and restring - when I can put the thing down.
I use 0.010" to 0.046 strings on my Gibson Les Paul which is pretty similar to my JTV-59. After a couple of weeks living with the D'Addario 0.010 to 0.046" gauge factory fitted strings I felt they seemed a bit 'stiff' so I changed them for a set of 0.009" to 0.042" D'Addario strings. I use 0.009" to 0.042" strings on quite a few of my other guitars but for some reason on the JTV-59 these D'Addario nines felt a bit too light so I ended up going back to 0.010" to 0.046" Ernie Ball Slinky which are fine. I'm not really sure why the original tens felt stiffer than usual - weird - and normally I have no problem with D'Addario strings LOL. BTW - a friend of mine tried my JTV-59 with the original D'Addario tens and without any prompting from me he complimented the guitar, the build quality and its playability but he said that the strings felt a little stiff too.
If you prefer nines, you shouldn't have any issues with them - maybe I was just having an 'off' day