Delaying paragon paths will have several effects, all of which will cause the player characters to be a bit weaker.
Paragon paths give two class effects at level 11 or 12. These are roughly equivalent to feats in power. In addition, paragon paths give a level 11 encounter power and a level 12 utility power.
These deficits could possibly be offset by granting the players temporary feats and/or powers until they get their paragon path. The powers might be general powers that you create for the characters based on their role, or they could be an additional encounter and utility power from a lower level.
As for how to pick the paragon paths in play, there are several ways to introduce the paths in a more organic way, ranging from open ended to binary choices. You could let the players choose during play and having them justify what caused their character to go in that direction. Alternately, you could have each player select two possible paragon paths, and then create situations during the campaign that cause them to go with one or the other.
I think this could add to the immersion if you explain it to your players and execute it well.