You can replace the switch with another router, but that alone will do nothing to fix your problem as the original router is still blocking PC-1 from accessing the network drive and printer.
You will need to configure the original router to be a wireless access point, this strips away the traffic routing functions and makes it just a wifi extension of your network. If you search "congiure <router manufacturer> as an access point" you should find more detailed informaiton on the process. The main things you need to do is dissable NAT and SPI firewalls, dissable dhcp, set the access points IP address to be in the subnet of the new router (but outside of the dhcp range), and plug the ethernet cable into a LAN port instead of the WAN port.
The only mild concern is if it would break your USB print server function. There is no reason for it to, but I have seen weirder/stupider things before.
If you utilize wireless and the wifi being in its current locaiton is ideal, then the router/access point option is the best one. If you dont need wireless or you need it more in the switch/pc-1 location then the usb-network print server is the simplier option.