I wouldn't let anyone but a trained vet sedate my horse. (You wouldn't want anyone but an anesthesiologist sedate you, right?)
I've never heard of a barn "requiring" you to clip your horse. That seems odd.
How much longer do you have before you have to clip? At the most, it really shouldn't take more than a couple weeks to get your horse used to a clippers. Are you sure your timing is correct for the desensitizing training?