I'm trying to find a way to get my 240 Sundancer to turn sharper when
leaving the slip. Would lowering one trim tab have any affect on
turning while moving at slow speeds?

No, they won't do anything to help rate of turn at slow speeds.

Any other suggestions for making
it manuever better at docking speeds?

More practice. Combinations of more power and better use of reverse would
probably help. Going so slow you don't have enough control is a problem.
Going faster and being ready to apply reverse generally helps more. When
you go "too slow" you run afoul of currents, prevailing winds and the
general lack of keel (compared to a sailboat). Those combine to push you
around in ways that generally don't help what you're trying to accomplish.
Power, under control, is your friend.