"You can't convince a believer of anything; for their belief is not based on evidence, it's based on a deep-seated need to believe." - Carl Sagan
Notice the dialog is not asking for a specific "SHX" file, it's only asking for a font name from the list of fonts (either .shx in the support file search path, or .TTF as installed in Windows)
When there is a missing shape file, you are prompted with a standard Windows file selection dialog, to select the actual SHX file that is missing. This is what the original message said.
A little late, but here it is if you need it.
To clarify, it is indeed a complex linetype Shapefile.