It's kinda of a dumb question for which I apologize in advance but how do I attach an wrist strap to my iriver Clix 2 (the 2 GB version)? There is no "hole" in it.
I don't wanna ... drill one.

My silicone case has a tiny tab with a hole in it that takes the supplied lanyard - for hanging it around your neck. A wrist strap would work with it in the same way, if the cord would go through a small hole (< 1 mm).

After having one for a couple of weeks, I can recommend a silicone case. It does reduce the cuteness factor of the clix a bit, but it makes it much harder to drop. And dropping your clix could disfunctionalise it permanently.

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Clix 2 8GB Red Line Zen Touch 20GB
Shure SE530 Shure E2C Creative EP-630

Aha. Thx. So ... Only with a case. Good to know.
I kept looking at the tiny hole in the back next to the headphones jack and kept wondering why is it there.

Yes, I haven't worked out what that recess is for yet. Funnily enough, my silicone case (yes, I just had to mention it again) has a hole that lines up with it. But not a hole for the microphone....

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Clix 2 8GB Red Line Zen Touch 20GB
Shure SE530 Shure E2C Creative EP-630

I believe the recess is for a combined headphone-lanyard accessory, it clips into the recess so that the headphone jack isn't taking all the weight / gives it a bit more security.