I'm really not sure what's the difference, both seem right.
The meaning is that the object has a shade of green upon it.
A side story - when I was learning Latin, I had trouble figuring out how to translate the ablative, a case that was often translated with by or with. So, for example, does
rēx armīs mīlitum interfectus est
mean "the king was killed by the weapons of the soldiers" or "the king was killed with the weapons of the soldiers"? Latin grammar might break it down further as an "ablative of agent" or "ablative of instrument," but in English, both seem to work with slightly different connotations:
by - "4a : through the agency (see agency sense 3) or instrumentality of"
with - "4a —used as a function word to indicate combination, accompaniment, presence, or addition"
So the prepositions can sometimes overlap in usage in English. In the case of shaded by/with green, by has a more active or instrumental sense than with - by more strongly suggests that something was shaded using that object. It is easier for an object (a pen, a tree, a pigment) to have this instrumental sense than qualities like color. So if you were wanting to emphasize the technical process of making something green, and readers understood the physical process involved, shaded by green could work, as used in this 1870 issue of Pharmaceutical Journal:
Yellow shaded by green
But note how uncommon this is - in several pages of Google results, "shaded by green (noun phrase)" was much more likely to show up, where, for example, "shaded by green trees" denotes the trees (which happen to be green) shading something. Something is shaded by an object or instrument.
When discussing color without a noun, shaded with green is much more common. The green could be merely present or added (M-W 4a) as well as agential or instrumental (6a). In this way, it denotes more generally the color of shading. Here are a few examples:
Decoration, 3 large white vine initials shaded with green and brown, on a pale mauve/brown, blue, and occasionally green shaded ground (British Library)
The Iva1 ORs (mouse OR families 258 and 259) are indicated by open diamonds and shaded with green (Nature)
Summer Pink - rose pink center and midribs, shaded with green towards the edges and outlined in emerald green
In short, with generally works. Occasionally, by works. And, as Benjamin Harman points out in a comment above, other prepositions may work. (Shaded in green, with in having a similar sense of medium or instrumentality according to M-W.)