I'd just send Dowly waaaaaaaaaaaay cheaper
But corvettes and frigates would do the job just fine. The thing is the DDs probably can't patrol the area due to their small numbers so the only way to make the transit off the coast of Somali safe is by means of escort. Or even better a deployment of small aircraft carrier or attack helo carrier but this would cost too much money.
Perhaps a psychological warfare of some sort is needed to deter some percentage of pirating. Send in a seemingly precious ship off the coast of Somalia only that the ship is loaded with special force team(GIGN, etc) so making the ship effectively a mouse trap . . .
but of course it's more risky . . .