Can I use a 28 VDC 10 A relay to toggle a 10 kV DC 0.03 A source?
No, the contacts will arc across and it will likely arc to the coil as well. Very, very dangerous. 

A commercial relay properly rated to switch 10kVAC will probably cost in excess of $1000. There are some DIY approaches, but better suited for non-novices. 

You should consider switching the primary, but being an inductive load that relay may not be acceptable.