I am a professional technical editor. I've been doing it for almost 16 years and I still need to be very careful about how I introduce my skills to a new client.
The best way I have found to do this is to ask for forgiveness, not permission. The next time they give you something to proof, bleed all over it. And yes, do it in track changes. Show them all the improvements you can make and then quietly tell them when you give it back, "These are only my suggestions. Please feel free to review what I've done and accept/reject at will. I hope you find this helpful."
I find more often than not that authors inexperienced with working with an editor have no ever-loving clue how much you can help. You approach it as a "look how much better this can be" not as a "look how much better I am at this than you."
Once they realize that you can take the odious task of writing completely off their plates, they will get excited for two reasons:
1) I've found that tech people usually loathe writing. If they don't have to worry about the writing part, they can focus on the part they like to do.
2) It's usually far more acceptable for a trusted employee to see glaring, embarrassing errors than it is for a potential client to see them. By helping them avoid the embarrassment, you are pulling double duty by adding value and avoiding professional blunders.
Good luck with this!