Do you have firewall on your Mikrotik that blocks access to File and Printer Sharing on printer computer?
If not, you should be able to access shares on that machine via the router.
Don’t drop it? By default the firewall permits all packets. So if the packets are getting dropped, they’re getting dropped because you told the firewall to do so.
If you need specific help with your specific firewall configuration - that’s going to be impossible unless you share your firewall configuration.