How unsafe is it to use a 10 amp fuse with a trace designed for 4 amps?

If you are able to change the fuse it seems like that would be easiest and kind of a no-brainer. The fuse always needs to be oversized a bit to avoid having it blow when there is no fault. Fuse manufacturers have guidelines for this kind of stuff. For a 4 amp circuit, maybe a 5 amp fuse would make sense. But check it yourself.

But if you don't want to change the fuse, then you kind of have to do a hazard analysis. What is the fuse for? Usually they are to prevent fires. If there is a short, will the 10 amp fuse blow before the trace blows? Probably. You can test that. This is the low impedance short test. You put a very low impedance short (in this case, say, 0.1 Ohms or less) such that the short circuit current will flow through the trace. Probably the fuse will blow very fast under these conditions. Usually a low impedance short is just a wire jumper. Even if the trace blows, that may be OK because once it blows the current will drop to zero and there is no safety hazard.

But what if there is a failure that doesn't blow the fuse? The so called high impedance short. How can you test for that? You apply a current of say, 1.5x the fuse rating using a controlled current source. Run that current through the 1mm trace for about two hours and note whether any hazardous conditions occur (does anything get dangerously hot or smoke or whatever?). If not, then you should be reasonably safe as far as thermal hazards go. If you don't have a current source, you can possibly approximate one with a voltage source and a power resistor. The important thing is to have the current flow through the trace.

Why 1.5x the rated current? Fuses do not blow instantly when the current is just a bit higher than the rating. Usually fuses are guaranteed to blow within a matter of seconds at 2x the rated current. But a 10 amp fuse may pass 10 amps for many hours and not blow. It may even pass 15 amps for a pretty long time. So 1.5x rated current is just kind of a round number between 1x and 2x. You usually want to keep the fuse either below 80 percent or above 200 percent of its rating. Otherwise you are not sure whether it will blow or not. That 80 percent is not a hard and fast rule. Just an estimate.

Conducting these tests is potentially hazardous. I am not just saying that. If you do it, please think through how you will do it and at a minimum make absolutely sure you have a way to de-energize the device remotely from a safe distance, and are able to extinguish a fire if one should occur, before the fire can spread to other areas. Consider also how you will escape if there is a lot of smoke (after de-energizing the device).

You can try to calculate how hot the trace will get analytically, but testing is another option.