Non-selective β-blockers like propranlolol can be prescribed to reduce essential tremors. They will reduce hypertension, cardiac output, heart rate, etc. For any sport that requires you to stand motionless, this would be a performance enhancing drug.
In terms of giving it to patients, if someone gets it that has a normal blood pressure, it can drop that pressure below a safe level... which is not good, hence the reason for checking vitals prior to administering it.
From what I just found, the Bronze medal in the 10M air pistol went to Jason Turner, of the USA.
Alcohol, in fairly low doses, also can effectively reduce tremors, which also improves some accuracy. It's also a performance enhancing drug in that context. It doesn't impair anything, but it does smooth out the tremors. It also metabolizes pretty quickly and unfortunately, it's also extremely easy to step beyond the point where it "helps" performance and into the realm where it impairs. The β-blockers don't metabolize as quickly and they're easier to control the dose and effects.