rinse your face with water if possible very gently but If you cant then idk

I work 24 hour shifts one day a week. This interferes slightly with the regimen in that I miss it one night a week. I don't have time at work to perform it. Nor am I comfortable working without makeup. Will this hinder my progress?

Well, I think it will interfere somewhat since you won't be using it for a full day. Do you have time to wash your skin at all with a gentle cleanser? Or at least just apply the regimen just once that day?

I will be washing my face prior to the start of my 24 and at the end of it. So I will only be missing one night per week.