In a two-body system it doesn’t matter what you do; gravity is a conservative force so conservation of energy demand that you leave the body’s SoI at the same speed you entered it (in the body’s frame of reference).
You can lose speed or alter course relative to another body in a single encounter, and those changes can reduce speed in future encounters, but if you’re on an escape trajectory heading in you stay in one (without forces beside two-body gravity, which is a pretty safe assumption 11 AU out of Saturn doesn’t come close).
You can lose speed or alter course relative to another body in a single encounter, and those changes can reduce speed in future encounters, but if you’re on an escape trajectory heading in you stay in one (without forces beside two-body gravity, which is a pretty safe assumption 11 AU out of Saturn doesn’t come close).