Why can't both ends of the wormhole be on earth in a lab next door to a newsagents with a contract with said newsagents to always deliver daily newspapers on time?
But you would need one exit to be accelerated to relativistic speeds to get a dilatory effect. If you could catch it there would be no relative difference in your frame of reference.
I thought you were meaning a wormhole accelerating through space to generate the dilation but I could have got the wrong end of the stick.