Is it possible to remove amalgams (mercury fillings) without drilling?

No: No it is not possible. No other way that i know of.

Not typically: Some drilling is required. However sectioning the existing filling and using hand instruments to remove the pieces along with the use of a rubber dam significantly reduces the amount of airborn debris and mercury vapor produced during removal. Advocates of air abrasion and laser technology suggests removal can be accomplished using those modalities in place of drilling but results r inconsistent.

No: Unfortunately, there is no way to remove any filling, amalgam or otherwise without using a handpiece and drilling it out. However, there is no reason to be concerned about this process. I would guess that you have concerns about mercury? There are many methods to reduce vaporization and ingestion during this process. Discuss your concerns with your own dentist for a thorough discussion of this.