The Ready State Virtual Mobility Coach is like having a virtual Kelly Starrett in your pocket.
The warm up should only be as long as necessary. If you are training people just a couple times a week with a few movements then just get their heart rate up (rowing, bike, jump rope or a bit of all three) and then a small handful of things that resemble what you are working on that day then get after it. Make sure over the course of the week the warm ups have exposed them to all the shapes the arms and hips can be in so you as a coach can note places they have trouble going and prescribe homework or cool down work to target them. No reason to make it more complicated.