In my opinion a skilled bullseye pistol shooter will shoot more accurately with one hand.
The key to extreme precision is elimination of all unnecessary movement. Introducing another hand, arm, pectoral, latissimus and so-on cannot be good. A one-handed approach means the shooter need only focus on the gripping fingers and his trigger finger. The thumb and pinky play no role.
I understand your temporary need for support, but that will go away. Holding the gun up will cease to be a problem and likely you will refocus your efforts on a firm grip.
What you will find is that when you shoot other disciplines that require 2 hands you will have a much better understanding of how to grip with the off-hand and what it is supposed to accomplish. You will find your accuracy greatly improved with 2 hands.
Hang in there!
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