From the outset, you can't prove that RFC 6979 was used. I.e. RFC 6979 doesn't provide provable security. If you want a proof that there are no covert channels, you need to implement some kind of interactive protocol between the signer and the verifier -- I'm not aware of any standard/popular way of implementing that.

What you can do is use a dice to generate a key and the sign a bunch of messages with your hardware wallet and a piece of software that you trust. You can then compare the two outputs. This gives you a probabilistic trust level (the more messages you check, the higher the likelihood of there not being a backdoor). (note: I implemented this logic [1] to check that three different RFC 6979 implementations were returning the exact same bytes).

[1] https://github.com/alokmenghrajani/decv/