Silver has 5% lower resistivity, so all else being equal would take more current to heat it to a given temperature, so the current rating would be higher (and cost a lot higher!). Silver’s melting point is also 123C lower than copper, so if subjected to a direct short the wire itself would melt and break the circuit sooner, though that is possibly of little relevance as unless mineral insulated the insulation will melt at a far lower temperature allowing contact between conductors and arcing, which I think is the main fire risk. Rather than silver conductors, a much bigger benefit could be through use of PTFE instead of PVC insulation, with something like 270C vs 60C max temperature.
But if the cable is standard mains rated flex with copper conductors and PVC insulation then indeed 13A would seem insufficient to protect fully from fire risk, should something cause a short circuit. (possibilities include something faulty with the mains socket of the equipment, or with the mains plug into the equipment, or if there is repeated flexing of the cable (unlikely with hifi gear) causing physical breakdown of the insulation, or if the cable lies against a very hot surface such as radiator feed pipe over 60C.) These conditions may seem unlikely, but the possibility exists and that is what the plug fuse is intended to protect against.
If a higher capacity fuse is better for sound quality, then the safe solution would be a higher current capacity flexible lead (cord).
The suggestion that a higher current fuse sounds better is consistent with the notion that a higher current cable from the fusebox sounds better than a lesser cable. However the suggestion that a thinner mains lead is better is inconsistent with this.
Considering all the above, the best thing to do would be audition various mains lead with different thicknesses conductor each with the appropriate size protective plug fuse, to find which works best with the particular mains supply in question. Given that flexible cables can be bought in a wide variety of conductor thickness (in UK commonly 0.5, 0.75, 1.0, 1.5 and 2.5mm^2) all at negligible cost for just a metre or two, and that it is easy and legal to connect into plugs. Making up such mains lead assemblies would be only a low cost to ask an electrician to do, though it is perfectly legal and easy to do as a DIY job for anyone with the basic ability/awareness. Finding appropriate fuse ratings might take a little searching, as may finding fuses: fuses are readily available in at lease 1A, 3A, 5A and 13A, and provided the equipment has its own appropriately rated mains protective fuse, as I believe is normal with Naim products - if not then don’t use a fuse higher than the equipment supplier recommends. In theory it wouldn’t matter if the plug fuse was higher rated than 13A provided appropriate for the flexible lead, and could even if appropriate be higher even than the consumer unit breaker as that would then be providing protection to the flex+fixed wiring circuit, however I say in theory because the question then arises as to the safety of the flex lead mains plug and wall socket combination under higher currents, and this would need to be known before exceeding a 13A fuse in a so-called “13A plug”.