Welcome to the forums @Arturos
If you want the result – after manipulation – to be vectors then you currently (as of 1.8.5) cannot do what you want with the Affinity applications in any way other than manually manipulating each curve.
If you don’t mind the result being a raster then, if you only have access to Designer, you could make your shape into a Textured Image Brush, apply that brush to another curve and then manipulate that curve. (See various forum threads and the Designer Help for Textured Image Brushes and Vector Brushes.)
If you also have access to Photo then you can use various tools – e.g. Mesh Warp, Liquify Persona, etc. – to do what you want.
Note: Other applications are available which can 'bend' vectors; they are well-documented in various other forum threads.
I am impressed how far ahead of time your planning goes...
I wanted to do an arc with arrow heads, but so I can easily change the angles later. It should look like the blue arc (I created with cutting a circle, so angles are fixed). I tried to use the pie tool and set the hole radius to 100%. Works in principle, but not in regard to arrow heads. When doing this both arrow heads overlap and only one is seen. This is how AD treads the start and end of the line, as can be seen with the red shape.
By the way, the same is - of course - true for the line caps. You cannot get butt cap equivalents on the pie, as neither bevel nor miter join would achieve this.
My suggestion is to tread the end of the line differently, when hole radius equals 100%. For this special case, I suggest to not draw the inner circle and the connecting lines, just the outer circle. Then the arrow heads should be shown correctly automatically... and the caps too.
Maybe this can be implemented easier than the arc segment pen tool...
