State law may or may not preempt local ordinances. It depends on the law and whether the state law is written in a manner to make it take precedence.
While 9.41.300 does mention other weapons besides firearms, 9.41.290 specifies preemption only in regards to firearm laws in compliance with 9.41.300. So no, the preemption does not extend to other weapons.
"Cities, towns, and counties or other municipalities may enact only those laws and ordinances relating to firearms that are specifically authorized by state law, as in RCW 9.41.300, and are consistent with this chapter. "
If it did not specify firearms, or said "weapons" instead, that would be different. But the preemption is limited to firearms only.