Well, I don't really like self-resistance like what you described there. Now, there is a huge difference between bodyweight resistance and self resistance. I like bodyweight exercises (pushups, chinups, weighted and unweighted) for main workouts, GPP or extra workouts. But "self resistance" I just don't think works well. Zatsiorsky has a good section of "Science and Practice of Strength training" dedicated to explaining the differences between bodyweight resistance and self resistance, and I don't think I can do an adiquate job summerizing it. So if you're really curious about why I don't like the idea of using one hand to provide resistance against the other hand, you can check out his book.
But, if you want another idea to strengthen the muscles that open your hand, without spending $20 (Outer Limit Loops) or keeping a big bulky bucket of rice (or sand) around, then try this idea: Just use a simple rubber band. Wrap it around your fingers and open your hand against the resistance of the rubber band.
I got this idea from Vince Dizenso, one of the best bench pressers in the world. He's benched 700+ multiple times in competition and in the gym, getting as high as 760+ in one competition. He's also benched 700 in single poly equipment, so no matter how you slice it he's a pretty strong guy. Can do 500+ incline benches, and 400-500 pound overhead presses from eye level up. Used to squat 700 pounds in competition before he hurt himself.
He had pretty bad forearm pain, and he said the elastic band worked pretty well. Again, thats a cheap, simple solution for the guys who don't want to pay a lot of money or lug around a bucket of sand. I still think the OL loops are the best, with rice or sand being a close second, and rubber bands being inferior (but still good) to both.
The problem with splitting up your training into "bodyparts" is that you tend to neglect important bodyparts that you can't see, hence strength imbalances develop. Even if you don't believe that compound movements are superior (which they are, and I'm glad you agree with this Neodavid) you still can't deny that when you do complicated multi-joint exercises like squats and powercleans, you tend to train most muscles in your body. This means you'll likely prevent imbalances from developing.
However, one thing thats hard to prevent is the imbalance of opening/closing your hand. Even if you train really smartly, with lots of compound movements, this is still a tricky one. Do what we talked about here, and you're all set.