Hi Jochen,
Self-signed certs (option 1) should work, but that's something you will need to agree to with the partner. Some companies may have polices against them. Either way, I would send them your public cert (and CA certs if you are using them). Most systems need it to setup access (or at least the DN patten). Just don't send them your private key (p12).
Thanks,
-Russ