I've been using 'Insect Eliminator with 100% natural Pyrethrins' by the brand 'Expra'.I only use a little bit when i have to and I've seen no problems with my IRN, but it does say not to use around fish tanks. It has no warning around pets like most fly sprays do so i don't know if its suppose to be alright or they just left that bit out.
Even though natural(from a flower) it is deadly poison. Especially if the birds eat the insects that are killed by it. The advantage of pyrethrin is that it breaks down relatively quickly after it is used - but until it does it is poisonous. And i dont know how much it would take to kill a bird. They only mention fish warnings cause it runs off your plants/lawn when you water it and goes into the water supply and kills the fish. They dont expect people to use it around pets, so they dont warn about it.
Natural does NOT mean safe. For example Belladonna is natural (also from a flower) and has been used for centuries to murder people.
For ants you can use a powder called Diatomaceous Earth (silicon dioxide). This is basically just old fashioned chalk powder - sprinkle a lite coating where the ants walk. This stuff is so safe you can eat it. It is not a poison, it kills bugs by drying out their "skin" - sucks the water out of them. Also kills roaches. You can find it at organic garden centers or you can order it online (one brand is called Safer, but any will work).
The only danger might be if the birds inhaled a LOT of the dust so it clogged their lungs - but this is highly unlikely if you sprinkle it gently low to the ground and there is no wind blowing it around forming dust clouds after it is down.
Also a temporary fix that sometime lasts a while - you can find the trail the ants use outside the cage and wash that path with a strong soap. This will remove the chemical path markers the ants put down to map the road to the food. They wont know where the food is until a scout redisvocers it.