In order to change this starter from having two connections to one connection - could I cut the second connecter completely off and solder the connecter that’s attached to the motors directly to the power switch?

This is showing the 2nd battery connecter that I would cut off(it’s also connected to the switch)

This is showing where I would solder the connecter that’s attached to the motors to the power switch

simplest way is to cut one of the deans connector out, and solder the 2 loose wire together.

Clip off Deans with 2 red wires(eliminating Deans's), Strip end of red wires, add 1.5" shrink tubing, Splice 2 red wire Together with solder heat up shrink tubing. Done