Back in the day when I learned soldering, the master told me that usually I need 3 hands:
One for the iron, one for the soldering wire, one for the piece that I want to fix (while the other piece is already fixated, for example the board)
Before I used the "3rd hand tool" with the alligator clamps, I often held the soldering wire with my mouth and moved it precisely into place. It takes some practising, but it is doable.
So maybe this is a way for you: always use that "3rd hand tool" AND use your mouth for the soldering wire.