Is the use of the word 'hence' improper in business writing?
The customer (in this case, the client) is always right. Or as a local retail outlet in my town puts it--etched in marble, no less:
Rule #1: The customer is always right.
Rule #2: If the customer is wrong, read rule #1 again.
Hence sounds perfectly fine to me. You've already specified the audience is a "business audience," so they are not likely nincompoops. Off the top of my head I can imagine a speaker saying in a motivational speech,
"Too many people don't bother to ask for what they really want; hence, they don't receive it. I say, only by asking will you receive. In other words, you have not, because you ask not."
Or,
"Company XYZ failed to set their sights on a goal which would both challenge and stretch them; hence, their bottom line last quarter was a big disappointment. If, on the other hand, they had set for themselves a challenging goal which would stretch them and in the process prepare them for even bigger goals, they could have avoided that disappointing quarter."