I followed the tutorial for generating a code-signing certificate using the YubiHSM Key Storage provider available here. After creating the Certificate Signing Request (CSR) with certreq -new sign.inf sign.req a new asymmetric key is created in the YubiHSM together with an association between this key and the certificate in the YubiHSM Key Storage Provider (KSP). After that, I am able to sign my binaries using something like signtool sign /sha1 <certificate hash> <binary name>.
However, when I export this certificate and import it to a different machine the certificate does not have an associated private key. Typing certutil -repairstore my <certificate hash> does not help. As far as I understand, the KSP only stores a link to the YubiHSM, not the actual private key itself. So I suppose I need to somehow create this association in the KSP.