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Assuming the shim doesn't extend past the top of the stem, you'll be able to use a normal 1,1/8" top cap.
No idea about the best approach for the star nut, but @roboto has a CP thread where one method is discussed.
If I have a 1 inch fork shimmed to 1 1/8 do I need a 1 inch top cap or normal one?
Also, the best way to get out a fucked star nut when access from the fork crown is not possible?