The quick answer is probably not. Tremors run in my family and I have them pretty bad - using a fork with my left hand is iffy for me. The tremors are not a matter of weakness.
For modest tremors you may want to look into the drug Propranolol. I've used it and it helps but has side effects - for me drowsiness was the worst part. In severe cases there are surgery options. It involves the brain so it's not a minor thing. I have an anesthesiologist friend who tells me it would be fun but I think he means fun for him, not me.
So what I'm wondering is whether this "test" can be adapted to become an "exercise". Will practicing with the test for some number of minutes a day condition my hands to stay more tremor free? That might be an interesting body hack.