No, it is not a safety issue, unless the fuse box is damaged or deteriorating. Fuses are actually more sensitive than circuit breakers; therefore, they are safer than circuit breakers.
There are two main issues with fuses. First, after a fuse protects your home from an overloaded circuit, you have to throw it away. So you may go through many fuses. Second, most insurance companies now require that fuse boxes be replaced with circuit breakers. We’ll check the local electrical codes for your particular situation.