I wouldn't bother with the BB-pistol version of your gun. Dry-firing your real gun is probably more real than live-firing your BB-pistol. For dry drills, I still suggest a timer and put it on par just to give yourself a goal. If you find you get clumsy with a reload, get a bad grip on your draw, or can't find your front sight on a target transition, increase the par time to the point where you have enough time to execute the movements perfectly. Then slowly reduce the time again. Keep some records during your dry drills, just as you would with live drills. You want to keep track of your progress to see if you're doing things right. It also helps motivation if you actually measure your progress and see it happening.
As Don mentioned, safety is important when doing dry-fire. Double, even triple check your gun and mags before starting your practice, even if your gun never even came close to ammo since your previous practice the day before. You shouldn't even have ammo around in the same room.
Try to do your dry drills every single day, even if you can only get 5 minutes of raising your sights and aligning them at a light switch on the wall over and over. If you miss a day or two it's not a big deal, but doing regular practice is important. It's exactly the same as learning to play a musical instrument like guitar or piano. Little 20 minute sessions everyday are much more effective for teaching your mind and body these sorts of skills than doing a 3 hour marathon once a week.