If not, start by putting the neck in and clamping it down tight. You want to make sure it is seated really firmly in the pocket. Then put a strait edge on the top of the neck so that it extends out to where the bridge is. How high is the strait edge over the top of the body? Is it too high for the bridge?
This guitar uses a Gibson tune-o-matic style bridge. That's going to sit a bit higher than a Fender style bridge, so the neck needs to be at a bit of an angle. I have a bass with a standard Fender j/p bridge. The E-string saddle is about 13 mm above the wood. On another bass with with a tune-o-matic bridge, the E-string saddle is at 23 mm above the wood.
So if the neck angle works with the bridge, great! If not you probably will need to shim. I am not sure I understand your reluctance about that. Looking at the photo, it looks to me like a shim should work if you need it. You could dry fit the with a piece of veneer to see how it effects the angle. The veneer I use is 0.5 mm so you can build up in very small increments until you get to the angle you want. If you don't have veneer, some people use playing cards.
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