Even though Inkscape doesn't support changing the type of stroke, you can still get the end result you're looking for. There may be more than one way, but what I do is:
- create the shape
- select the shape (F1)
- copy the shape (Ctrl + C)
- paste the shape in place (Ctrl + Alt + V)
- change the stroke width to 2x the inner border you want (e.g. 2px if you want a 1px inner border)
- select no fill for the pasted shape
- now select the original shape
- paste the shape in place again (Ctrl + Alt + V)
- select the pasted shape and the stroke shape (holding shift down)
- set clip (select menu Object > Clip > Set)
This will clip the border shape, omitting the extra (outer) part of the stroke.