I did some testing and crunched some numbers over the weekend.
I suspect there's still some factor(s) I haven't thought of that I'm not taking into account, but here's what I've found so far.
I did the same trick for most of the Tier 5 vessels, where I got their turn rate while completely unskilled, and again while fully skilled. Then I worked out the turn rate gain per skill point, and then divided that by the base unskilled turn rate. I then averaged any differing results together, based on ship class (cruiser, escort, science). Here's what I got:
Cruiser Average = 0.00087968212535387050622507686166667
Escort Average = 0.001122822737848204741243790479
Science Average = 0.00105894805832726163454301388125
I suspect you could get away with using an abbreviated average, such as:
I'm not sure how useful this is, because it requires you to know what your turn rate is at your current energy level with 0 ship command skills, and what it is at 100 engine power. I also have only accounted for basic impulse engines, and not ones with Turn modifiers, nor have I accounted for RCS consoles. Also, it's certainly not perfectly accurate, though as I stated before, this is likely due in part to rounding issues, as the in game display of turn rate is limited to one decimal place. Still, I think that it should get you within 0.1 degrees if you have all the info you need.
One other thing I don't think I've mentioned yet, I have determined that your turn rate bonus from the various starship command skills is constant, regardless of our engine power. . i.e. If you have enough skill to gain 3 degrees of turn rate, you'll have 3 extra degrees of turn rate both at 25 engine power and at 100 engine power, then you would if you had no skill.
One very interesting thing I discovered was the unskilled turn rates at exactly 100 engine power tended to be whole numbers, at least for the ships I tested:
Multi Vector Advanced Escort / Fleet Escort / Advanced Escort - 27.0
Tactical Escort Retrofit - 31.0
Reconnaissance Science Vessel - 23.0
D'Kyr - 17.0
Deep Space Science Vessel - 19.0
Long Range Science Vessel Retrofit - 21.0
Assault Cruiser / Star Cruiser - 11.0
Exploration Cruiser Retrofit / Dreadnought Cruiser - 9.0
Advanced Heavy Cruiser Retrofit - 13.0