Is there a safety issue with round fuses versus circuit breakers?

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. Therefore you may go through many fuses. Secondly, the majority of insurance companies now require that fuse boxes be replaced with circuit breakers. We’ll check the local electrical codes for your particular situation.