Is there any work around to show the UI task links(not a quick task) in Records?

Create a standard GRID SAIL report showing the necessary information and you can display it within Records. Records also allow for additional Record Views that you can utilize for this purpose.
In general, the SAIL code is uniform across the board irrespective of where you use it. The only difference being the context that you can provide - which you get in Records and not in Report directly.

Create a standard GRID SAIL report showing the necessary information and you can display it within Records. Records also allow for additional Record Views that you can utilize for this purpose.
In general, the SAIL code is uniform across the board irrespective of where you use it. The only difference being the context that you can provide - which you get in Records and not in Report directly.