Please post a screenshot of one of your level concept designs so that we have something to look at.
From what I understand of "white-boxing," it is the method of building and play-testing a
preliminary version of a level so that you can
feel if the original design is lacking or exaggerating in any quality such as difficulty, navigation etc. The name comes from the way that some level designers build this preliminary version out of white boxes and polygons of varied sizes.
It's not related to the method that you will use to build the final levels, such as "tiling" or hand-painting them. I also believe that you can apply it to 2D games: You would build a preliminary version of your level with the platform\collision information so that you can play-test the level without spending considerable artistic resources on polishing something that might receive tweaks and modifications for improvement.
A game that has beautiful hand painted art is Rayman Origins. The concept artist for this game was Floriane Marchix:
![water2colo_282_29_cofgdgpie.jpg](http://s29.postimg.org/l1cvjeqfb/water2colo_282_29_cofgdgpie.jpg)
![water2colo_282_29_cofggpie.jpg](http://s29.postimg.org/fbwmz3k93/water2colo_282_29_cofggpie.jpg)
While you can use tiles of any size that you want and not necessarily of a "pixel art size," if you're going for a hand painted style it will make more sense to go for hand painted levels.
Based on the display ratio of your game (for example 16:9), you can define the general layout and structure of your levels as simple polygonal shapes - you can also play-test these as your levels as if you were whiteboxing.
You know how many "display screens" long each section of your level is supposed to be, so when you want to know their dimensions in pixel units, you can calculate these based on the
highest resolution that you are willing to support such as "full HD" ( 1920 x 1080 ), for example.
The logic is this: When you are designing the level you are not concerned about pixel sizes, you are just concerned about how much the elements occupy on the screen - a generic, 16:9 screen without a defined resolution. But your artists need to know the exact dimensions in pixel sizes so that they can paint your level. When you want to convert the dimensions to pixel sizes, if a platform in your level is two display screens wide then it should be a graphic 3840 pixels wide (or 1920 x 2) and have some arbitrary height in pixels that you decide (preferably a magnitude that goes beyond the bottom of the screen region at that point in the level so that the player does not see the edge of the graphic).
Then you can render or save this polygonal layout as a single image or break it down into separate images, and send this material to your artists to work on and paint over them.