You can't hurt anything to do what KISS or Mr RB are talking about. Or a softstart as dr pepper recommends. The simplest softstart one can make is just a high wattage, low resistance NTC thermistor. These have a high resistance at first, so limit inrush current. But as the current starts to flow, they heat up. Having negative temperature coefficient (NTC) means they lower their resistance when they heat up. The subsequent drop in resistance allows for full system current with minimal circuit impedance. It's a single cheep part, I see them all the time in CRT displays. The only thing is they can get quite hot. Sometimes they would even get hot enough to unsolder, and thus need to be welded/socketed to be reliable.
*HERE* is what I'm talking about. If you have a business, you can even request free samples from them. But you can also order them from DigiKey, Newark, Farnell, etc. with the links on the left hand side. They make units that you can use to limit current for either the primary or the secondary. Either circuit location should work to limit inrush current through the diodes.