Cleo just last night ate a full grown cherry shrimp about the length of her head. First she dismembered it. Then she paraded around with the tail in her mouth for half an hour, looking very pleased with herself. Then she ate it.
These fish evolved to eat all kind of bugs and critters, so I don't see a problem really with feeding them small bugs that might very well fall in water outdoors and be eaten by fish. Mine have eaten spiders, craneflies, mozzies and larvae, small moths and yuck - the odd housefly - all by chance fallen in the tank. To date, there's no ill effects at all.
Except -- yes, I have seen a lot of mold and nasty crap in those cricket tubs - I used to buy pinheads for my frogs, and had a heck of a time finding a LPS who kept clean crickets. In the end, we had to go to a specialty reptile store.
Sadly, I'm nowhere near there now, so I won't buy crickets in case of mold and disease from unclean conditions.
Try some wingless fruit flies or raising your own mosquitos - or if you're set on pinhead crickets, at least find a good reptile store that is concerned with pet health and keeps them spotless and regularly replaced (ie, NOT most chain store pet supply places) and then keep them as cleanly as you can. That way you can control how clean they are when they hit the tank.
Oh yeah, and get some high protein betta pellets. These are a complete diet, and mixed with lots of live food are the best chance of good nutrition for your fish.