I. Diving Physics
II. Diving Physiology, Decompression, & Emergency Management Procedures
III. Diving Equipment, Systems, & Procedures
IV. Practical Use of Diving Equipment
There is some percentage of all of these that a well trained recreational diver will easily understand and there are some that are quite different or not entirely obvious until explained in context. I was a certified diver with 8 years of experience from an old-school 1960-era SCUBA course and obsessively studied the US Navy Diving manual before starting the Navy 2nd Class Diving School. As a cocky 19 year old, I started school convinced that "I already know all this crap". I did know a lot, but far from enough.
Surface supplied diving and the objective to accomplish work instead of entertaining myself shaded everything I "already knew". Diving physics is the same but context can change -- have you ever considered that a hose failure at the surface can fill your hat with your soft tissues because your check valve failed?
This still applies to modern hats except helmet squeeze can happen a lot faster. Related differential pressure risks need to be discussed in context so they are in the front of your mind instead of just having a theoretical understanding after something bad happens. Many "gotchas" relate to work-support systems like air lifts, waterjets, burning/welding, and 20,000 PSI water blasters.
A mixed gas tech diver probably has a greater understanding of diving physiology than some diving supervisors, but decompression and emergency management is very different. Very little diving is done on Nitrox, but a great deal of decompression is done on pure oxygen and in chambers. It varies by jurisdiction but the vast majority of mixed gas diving is in saturation. You probably have more to learn about diving equipment, systems, and procedures than physics and physiology.
To be sure, having your background will make everything
MUCH easier to understand and, more importantly, relate to. A great deal of our concerns as Scuba divers are eliminated or shifts to your tender/bellman and the dive super. Of course you need to have a complete understanding, but a working diver's focus is very different.
Of course the type of commercial diving you are doing matters a lot. Scraping boat bottoms and changing small props won't be much of a transition. Shallow air diving on a big salvage project is another world, as is saturation diving for the offshore oil industry. Please don't take this as
elitist crap from an old commercial diver. Commercial divers are not prepared for technical Scuba diving just as neither of us are prepared to be military combat divers. Knowing how to change light bulbs doesn't make someone an electrician.
IMHO, your risk of missing some small but critically important insights by trying to skip subjects that are familiar is very high.
BTW, I wouldn't consider commercial diving until the price of oil recovers. The entire market (civil engineering, ship's husbandry, etc) will be flooded with lot of highly accomplished oilfield divers while oil is below $40/barrel.