For testing the security of a service using mTLS for authentication, I need a client able to send the correct client certificate but then using the wrong key (i.e. a private key that does not correspond to the public key of the client certificate).
I want to make sure the tested service will fail the validation of the CertificateVerify message (a message that contains a signature made with the private key, and meant to be verified by the server using the public key of the client certificate). I can’t just do:

curl -k --cert client.cert --key wrong.key https://myservice

because curl sees the private key is wrong and won’t shoot the request:

curl: (58) unable to set private key file: 'wrong.key' type PEM

I was expecting the request to be shot and get an error from the server because the signature in the CertificateVerify message wouldn’t be verified by the server.

What tool can I use to make my test?