UPDATE: WORKS!
What I did:
su cmk ssh -i checkmk_ssh root@<target-server>
Asked me to trust the fingerprint. YES. Now it works!
Edit: Here the full command for anybody with same problem:
ssh -o StrictHostKeyChecking=no -i $OMD_ROOT/ssh/checkmk_ssh -T root@$_HOSTADDRESS_4$
Thanks @aeckstein