"Some of the metric units are awkward "
Being educated in metric, I tend to disagree; I find the imperial units to be awkward
Not only will you have to watch the difference between Newton (force) and kg (mass), you'll have to watch the difference between meter, second, etc... Newton and kg are completely different things, not just different units scaled by 10 (9.81).
"I would absolutely refuse to use a formula unless it specified all variables and their units."
I go further than this: I refuse to use equations/formulas that I don't know the theory that lies behind it, of. Often the theory makes lots of assumptions about the real world, which seep into the equation. And from a simple, mathematical-looking equation one can't determine what were the assumptions that lie beneath it. And whether the assumptions are valid for your specific problem.
As for as those silly formulas with constants in them to make up for the use of funny units (feets, inches, pounds, square yard per foot-poundal, etc.), they're errors waiting to happen.
And as far as horsepower goes: which of the three (3!) definitions and values do you refer to...
Keep it simple, keep it metric & SI.