Currently, it is not possible to reduce the Minimum Width Property of the PART_VerticalScrollBar part to 0.

If I remember correctly from a massive headache from trying to figure this out from working on the dev side many years ago, this is because the Minimum Width for this is set in some background/base theme settings or something similar...which was hard to find on the XAML side, but which I believe is not at all possible to access in Studio.
This, if I am assessing things properly, results in there being no way to set a Minimum Width of 0 within Studio.

See attached video for this in action.

Note that values above 0 can be set.
Note that this only seems to occur within the context of a ScrollBar inside of a ScrollViewer. An independent Scrollbar placed on a Page does not suffer from the same issues.

Repro Steps:

1) Create a Studio Project Containing a MainPage.xaml
2) Introduce a ScrollViewer to the Page, and create a new ScrollViewer Template from it. (This can be stored anywhere, and named anything)
This will open the ScrollViewer in the Inline Template Editor.

3) From the Navigator, find "PART_VerticalScrollBar" and select it to display its Properties Panel.

4) Under its Properties 'Layout' section, open the expander to reveal among other, the "Min Width' property.

5) Attempt to change the 'Min Width' Property to "0".

Observe how any attempts to change the Min Width to 0, are immediately reverted back to "17".

Expected Results:

The Minimum Width of a ScrollBar can be changed to 0 if desired.