There are no safe clot-dissolving drugs. The usual warfarin treatment doesn't dissolve the clot. It just reduces the risk of more clots. The original clot has to be broken down in a natural process called lysing, which can take months. As you can see on our Messages page, most victims report serious problems continuing long after the injury.
Warfarin is a blood thinning drug and rat poison.
If you are a person who tries to avoid toxic substances, you will not enjoy being forced to take rat poison. They don't need to worry. Pilots are at risk, too, and the first sign often is fainting. Dr. David McKenas, medical director at American Airlines, says that the most common causes of sudden pilot incapacitation are cardiac arrest, arrhythmia, and fainting. All I need is an aspirin as an antigoagulant.