It won't hurt anything.
Ideally you should make sure the impedance (ohms) of the replacement speakers match the impedance of the original speakers. Also, for best results; because the built-in amplifiers on arcade boards are relatively weak, look for replacement speakers with a high sensitivity rating (e.g., 90 dB or higher). Fortunately, most cheap coaxial car speakers are expected to be used with low powered amps, so they tend to have a high sensitivity rating by default.