I don't recommend skipping the previous-adventure backstory; it's a critical element of fate characters design, and the resulting aspects are the least important outcome. The most important effect is of tying the character's backstory in to the rest of the group. They have characters-they-know in common, and past history to draw plot from. This group generation of backplot is part of what makes FATE groups into a GMably cohesive story, not just a collection of interesting individuals.
I recommend running either two or the full three "adventures we had together" sessions. As you suggest, let the new character take aspects from these, but not the existing players. (Unless they want to swap out an existing aspect; it's a great time to allow that if new revelations about their backplot occur.)
For one of these sessions, I recommend re-discussing an existing past adventure that the rest of the group used for character creation, and revealing how the new PC was involved in ways that none of them knew at the time.
If they don't know each other yet and you want to run their first meeting - great, but it doesn't affect the character creation; run the backstory phases anyway. Just add an additional fact: they didn't meet, and don't recognise each other. That doesn't mean they haven't affected each other's pasts, it just means they don't know that.
("I was desperate; I threw the grenade out the window. I didn't learn who it hit until years later...")