Translation:I am going to a meeting with a customer.
It might help to realize that the English we are given here could more literally be: "I am going to go to a meeting with a customer".
It is the "to go" that is omitted in the Swedish, not the "going to", which in the Swedish here is the "ska".
In other words, there is a difference in English between "I am going" and "I am going to go".
Compare also "I am going to meet with a customer" vs. "I am going to a meeting with a customer". The first English sentence uses "going to" in the sense of Swedish "ska" or "kommer att". The second, it seems to me, uses "going to" in the sense of Swedish "går" or "åker".
It seems that my reasoning to use client based on the etymology of both wards, customer and client, which unfortunately apparently has not gone through, Client is a better translation since we are dealing with a professional relationship and not a store customer that buys goods.