In your user folder you can override the themes properties you want. In this case there is a minor problem as the scrollbar texture (the image that contains the scrollbar with the top and bottom semicircles) is quite dark, so although you modify the tint you can't get a light color similar to white unless you change that texture (image).
So the solution I pruposse is to create two new images (horizontal and vertical scrollbar) that are lighter, set it in the theme preference overrides and then (optionally) set the tint color you want.
- Locate your sublime User folder (Packages/User). The Packages folder can be opened using the sublime menu Preferences>Browse Packages, inside is located the User folder.
- Inside User folder create a directory called theme_override. We are going to place here all the files and settings of our theme that we want to override.