Sure they make wood that thin and if they don't that's were we come it. After all wood does grow on trees...
It's standard fare to have to rebuild a dovetail to a degree to reset a neck. This involves often gluing wood shims onto the the dovetail and then refitting, noting where there is a conflict (often using chalk), paring away in these area with a chisel, and trial fitting again repeating the process until the neck angle is correct including side to side and the dovetail has a snug fit when it's in place. That was a one sentence view of fitting a dovetail...
It's a complicated process if you are new to this and not something that I believe can be learned from someone telling you how they do it. Instead understanding the process, neck angles, how to use a dovetail chisel properly, grain orientation for shims, what materials work best for shims, use of "serviceable" glues and why, and some fretting basics as well since frets should be dressed after resetting a neck are important considerations. Experience is very helpful here too so is practicing on a beater with a proper dovetail.
If this is your first dovetail reset I'd look for a tutorial on the web to help you. It is one of the more complicated operations that Luthiers do and often benefits from lots of experience. Not sure that it can be properly explained in the one dimension of a forum but instead you would really benefit from seeing it done in person.
