Switching splines

[_Aka_]

Since I'm not using a spline controller from the examples, finding out list of all control points or firing an event on end reached isn't particularly going to help my use case 

You are right about the events, but the control points list is the list of connected control points part of a connection. Connections do exist without the need of a spline controller. So it might be helpful for your use case too.

Can you help me to get a reference of a CurvySpline via script?

yourControlPoint.Spline. As simple as that
https://api.curvyeditor.com/800/class_fluffy_underware_1_1_curvy_1_1_curvy_spline_segment.html#a7f76aef38bf7b32bd5fb85f9c3d0cf96

I want to know the CurvySpline that the player is standing on, how can I do this via code?

Use CurvySpline.GetNearestPoint on all your scene's splines, and see which one is the closest to your position
https://api.curvyeditor.com/800/class_fluffy_underware_1_1_curvy_1_1_curvy_spline.html#addc6dc085d215fdd925c4b9aafb7562c

I hope this helped
Have a nice day