1) I never use hard coded paths to any external resources. In my test for the .ICO it worked properly in 32 & 64 bit compile mode with no path (the opposite of what you reported).
2) The following up to #1 is .... Always link your .ICO file into the EXE using a .PBR file when you compile. I think that is the step you are missing.
FWIW: I always use .PBR's since the feature was introduced and I never have an issue with any external resources ... Nor do I hard code any path, to any image. The images are either linked into the EXE, a PBD or a DLL. Food for thought. 
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