Yes this will work.
We can assume the printers are network capable because they have Ethernet ports to hook up to the switch.
The Wi-Fi does not come into play as you are hard wiring into a switch-and they do not have to be the same subnet, in fact the hard wired printer can "be" on the Wi-Fi network as long as you make sure the printers get a valid IP host address in that Wi-Fi subnet.
Assign them static IP addresses in the same range as your wired or Wi-Fi network, or let DHCP give them an address if both are on the same subnet (a lot of routers are like this by default).
This is the only requirement from the router -other than it it simply working.
The switch does all the work.