Fin Animation pt. 2

Hey guys,

I already opened a thread about manta ray fins in here, and I’m very thankful about the help, but it somehow didn’t achieve the right results. So I try to start of completely new.

This symbolizes my manta fin with an arm that is going to be rotating back and forth around the 3D-cursor and he should produce a wave like motion into the fin.

So, my plan is to achieve this kind of waving motion by appling a wave-modifier to the plane (here) and then just keyframe the arm to the wave motion. Even though I already struggle to get the wave motion I would like to have I want to focus another problem here.
Some verticies should stay attached to the arm (just not wave with the rest of the fin). And I can’t do that without leaving a huge bump from where it stays still and where it starts to move. Can anyone help me, please?

Cheers Qlymax