The biggest thing the plants need to get used to , especially "leggy" ones, is the wind.
With a cold box/ cold frame, you can start raising the lid to let the breeze in on warm days, working up to taking the lid completely off, then removing the box completely, and then last to separating the plants .... though if they are still pretty "leggy",you may have to give then some shelter for awhile yet - a half shell of corrigated fiberglass, or row cover material on the trellis/cage, for instance.