my lecture experience is pre recording (they slowly started doing that when I left), so that might be a good way. Also for accessibility.
Cursive is faster than "print" and unless you are a medical doctor writing prescriptions quite legible.
Shorthand (I interprete this as meaning stenography) is a whole new writing system. If you mean just using abbreviations, condensing the explanations down to the essentials: sure, you have to do that anyway. Using cursive for speed.