Open circuits on the secondary of a CT are dangerous, so they should never be fused. However, they may not be able to source enough current to ever blow the fuses.
When a transformer scales down the current, it scales up the voltage. Current transformers are no different. If you open the output circuit of a live CT secondary circuit, you will generate high voltages that could damage the CT or other equipment in the system. The voltage drop across that 1 inch of primary conductor through the CT's core, will scale up by the inverse of the CT ratio. The current inputs on metering equipment are designed low-impedance like in-line ammeters, so they behave as close to a short circuit as practical, and don't generate a significant voltage difference. Unlike voltage measurement inputs, that have megaohms or gigaohms of input impedance, in order to behave as close to an open circuit as practical.
A CT output circuit should be shorted, rather than opened, in order to "turn off" the circuit. This is usually done manually, with CT shorting blocks or the test switch in an instrument-meter socket enclosure. Some CT's have built-in features that clamp the maximum open circuit voltage to be within safe levels. This is commonly the case for CT's with milliamp secondaries. For 5A secondaries, plan on providing CT shorting blocks for the outputs, so that they can be easily shorted when necessary to service the metering equipment.