Here is a way to remove 20 stickers.
To explain why the pattern works, consider the following cube with 18 stickers removed:
The cube has all its centre colours, so the 6 edges and 6 corners with 2 stickers have unique solved locations. The remaining 6 edges each have 1 sticker. There are exactly 2 ways they could be solved - the pattern above, or the following pattern:
Those edges have been moved in a 6-cycle, which is an odd permutation. Odd permutations are not possible on the Rubik's cube, so the two corners without stickers must also be swapped for this 6-cycle to happen. By putting back one sticker on the front corner, the corner swap is no longer possible, and this therefore forces the location of all the pieces. This added sticker also forces the orientation of that front corner, and the orientation of the stickerless corner is forced too because it is impossible to twist a single corner in isolation on a Rubik's cube.
Lastly, we can remove three centre stickers, in particular the blue, orange, and yellow ones. There are white-blue and orange-white corner pieces. This means the missing blue and orange centres must be adjacent to the white face, putting the missing yellow centre to the face opposite the white. Those two corner pieces also force the order of the orange and blue centres - if the colours were swapped both corners would have to fulfil the role of the orange-white-blue corner piece.
I don't think it is possible to remove a fourth centre sticker, but am not completely sure.
This reminded me of a sticker variation of the Rubik's cube that I came up with, that I called the Minimalist Cube. It came out of a similar idea, namely to use as few stickers as possible to still make an interesting cube puzzle. I ended up with this:
It uses only 1 sticker of each colour, but those stickers are each cut into quarters and placed on 4 pieces. Each piece has at most 1 quarter sticker. This puzzle does have multiple solutions, but also some non-solutions where a single centre is twisted 90 degrees.