Electrical – What fuse can I use to replace a Hitachi FN00373

The type and rating of the fuse you must use depends on your local regulations and laws, so it is difficult to help without knowing.

However, the regulations, no matter in which country, depend on physics - more precisely, they ask if the fuse will prevent the wires, switches and outlets from burning in case something fails and causes an overcurrent.

Despite your nice diagram, we can't tell what types (diameters/cross section) of wire are used in your installation, and where the wires are put. For example, different ratings apply depending on whether your wires are laid out in a stone wall or in a wooden construction, or in a wooden construction containing some thermal insulation making it harder for your wires to get rid of heat.

A typical installation in Europe, for example uses wires with a cross section of 1.5 mm² and fuses with 16 A. If the cross section of the wires is smaller, the fuses have a lower rating, too. If the wires are put inside of thermal insulation material (e.g. in an outside wall or along the roof), you may have to use 13 A or even 10 A for the same 1.5 mm² wire.

If you are not absolutely certain about your local regulations, please ask a professional electrician. If not done right, you put your house in danger of burning down.

Also, if you have sparks in your fuse holders, I think it's time to replace the entire fuse-and-holder combination. Sparks / arcing may cause very much heat, starting a fire in your fuse compartment!

Order the correct one.

It will work with a 500mA fuse, but you are putting the circuitry protected by the fuse at some risk due to the extra surge current possible. It's quite possible a component will blow rather than the fuse.
In general putting higher rated fuses in is a bad idea, though this is a smallish current and not too different, in extreme cases putting the wrong fuse in can lead to severe damage and possible fire.

So, while the fire or even the severe damage is extremely unlikely in this case, it's worth the wait to order a correctly rated fuse rather than put the wrong one in.