I've seen red and white currants as cordons but never black currants. Even as cordons they were just bushes on a "leg" but only had one "branch" instead of the usual half dozen. Clearly, with only one productive stem you aren't going to get the same yield as if you had six or eight. You can grow rd and white currants as standard bushes, with a 3 foot stem and the usual number of branches from the top of it, but you need a windfree spot.
Whichever style you choose, the cultivation for red and white currants is the same. Prune the tips of the main stem(s) in the winter by half the growth made this year. Prune side shoots that come off these main branches in June or July by cutting them back to 5 leaves.
Black currants are treated differently. They grow as a bush and have a third of their shoots removed each winter near to the ground, leaving two thirds behind. The idea is to stimulate the plant to make new growth as this is where they flower best.