I like on many components that I don’t expect to fail, to just raw dog it with no protection and replace the fuse with a slug (some think this is crazy, they are entitled to their opinion).
Reading through this thread leaves me open to the possibility that line fuses, being essentially variable resistors, may have a discernable effect on sound quality. If so, the difference is likely to be confined to fuse vs. no fuse, such that replacing a Bussmann fuse with an "audiophile" fuse is likely to be of no import since the latter is still a variable resistor. So I would have to agree with @carlsbad2 's quote above.
The best way to achieve this, though, is not to install slugs of various metals that can’t possibly make any audible difference, insofar as they are cradled in uber-cheap fuse holders made of common steel. Desoldering and tossing that 10 cent fuse holder and jumpering a length of appropriate gauge wire in its place, thus essentially hardwiring your power cord to your equipment's PCB as @mitch2 suggested, seems the sensible way to go.
As far as the Swiss Digital Fuse Box, it answers the safety question, but it seems highly unlikely that any device sitting inline with your power cord AND needing a 2nd power cord in order to function would not impart its own sound signature onto your system, just like power cords themselves have their own sound signatures.
Can the Swiss Digital Fuse Box be truly neutral sounding, or is swapping it for a fuse a case of robbing Peter to pay Paul, so to speak?
How about magnetic breakers, can they be free of effects on sound quality?
It is of course easy to take the fuse thing to absurd extremes that attract scorn and ridicule, but there is a sound case to be made for eliminating them - in a way that ensures safeguards remain intact of course, or are even improved. Fuses are not that good at doing their jobs anyway, so it is interesting to read about what can be done to improve upon the current situation.