Is there an external interface for getting to that point? Basically, what this site has always done is each user posting a thread containing all of their work, then people can click a link to download it and with some messing around add it to the game.
I'd imagine the simplest implementation from your end might be just to give a unique id on player cards for players/teams who have been shared online - and then have an option to enter a card number to go straight to that player.
A step above that would be to then have a URL structure on the PC version of the game (or to a web interface for your account on the console versions?) that could then launch the game straight to that point without manually entering it.
Also - unrelated suggestions:
Could the randomiser be weighted on nationality and age? Two screenshots attached to demonstrate the point - the ages aren't bounded in any way and non-cricket playing countries appear just as often. Ideally the names would be somewhat linked to location as well, so you don't get as many Craig Smiths from Afghanistan.