It's almost certainly impossible.
With symmetric encryption, both the encryptor and decryptor need a copy of the same key- that's what makes it 'symmetric'.
But with asymmetric encryption, the keys do not match. This means you can encrypt or sign the data with your private key, and then keep it private. The matching pubic key will decrypt or verify.
The device would not have a copy of the private key in it, so it's unlikely it will ever leak.
