Whether you can do this without a router between the networks depends on the NETMASK applied to the network.
Check your PC's network settings. As well as an IP address, you get a NETMASK that should normally be
255.255.255.0 indicating that all addresses from
192.168.137.254 are reachable without routing (0 and 255 are special addresses).
If that is the case, the printer only needs a single IP address and it will be accessible from both locations.
However, whether it can cope with output coming from two locations is another matter. It should if it is networked.
0 in the example netmask given is some other number, then the two parts of the network may not be reachable without a router. Let us know what the netmask is for further help.
Incidentally, a switch would not help you as this only switches connections from one device to another on the same network ("hubs" were used before switches became cheaper). A router is what "routes" between networks.
If the printer is not natively networked, then it presumable is connected to a PC. The same rules apply as outlined above but applying then to the PC rather than the printer. In this case, the PC needs to share it's print queue. Windows desktop OS is capable of supporting up to 10 simultaneous connections.