Hey Scott! Yeah, I would store the whole thing in the fridge. They'll be fine if you don't, but if it's gonna be awhile before you use them, it'll keep them from getting sticky if it's really hot wherever you have them.
Even if they get a little sticky, they "un-stick" just fine! I've had a big zip-lock bag full of SS that's rode around in the car with me since Feb... you can imagine the freezing, un-freezing, scorching hot...not to mention how my car smelled! They still catch fish, though!