Good idea CC
I'm watching Mythbusters right now. GBD if you can't get that much silica gel then use plain ol powdered cinnamon. It's hydrophilic and will absorb the moisture just like the silica gel. Try to use saran wrap and pour a couple of inches all around the handle then saran wrap it so the cinnamon absorbs only the moisture on the rod. Your rod may end up being the sweetest rod on the river....lol.
Try the non-destructive first and if they all fail then you may have to take to a repair shop to get it re-corked. But I'll keep lookin for you.
Good luck.
EDIT: not hydrophilic, it's hydroscopic (absorbs surounding moisture). My apologies. I should have know better then to be so careless. Wrap it and leave it, just not sure how long. It will take some time like a few days, I think.