...... People who came to Karachi actually came through Punjab. On their way to Pakistani Punjab, they passed through Sikh areas in trains, where they were slaughtered in LARGE NUMBERS......
There were two major waves of Urdu Speaking People USP migration.
You are correct that the first wave came through in 1947 from Dilli to Lahore. These were mostly the federal government employees in Dilli offices who had opted for service in Pak. In fact their train was the first to be bombed by Patel's goons in order to make sure Pakistan won't have functioning government offices.
The second wave of USP migration started after Liaqat Ali Khan became all-powerful PM following Jinnah's death.
This is the time LIK "imported" millions of USP who mainly used Khokhrapar crossing. BTW the second wave of USPs came to Pakistan when the 1947 riots had long subsided.
The second wave of USPs formed the majority share of the ancestors of modern day USPs who now live mainly in Karachi and Hyderabad.