Essential oil question

Hi all, I have two beautiful budgies that live in my kitchen/living room. I’m careful not to use anything scented, chemicals or essential oils etc. Unfortunately I also have a few cockroaches 🤢

I’ve read that eucalyptus and tea tree oils are a natural deterrent for cockroaches. If I put some around the kitchen say in cotton balls would this be okay for the budgies?

I’m wondering if because eucalyptus and tea tree are native to Australia, they might be okay. I wouldn’t actually spray it near the birds just pop some in cupboards and corners away from the cage.

Pic of Buddy and Winter because they’re cute!