Having your PC on a different subnet will not limit your ability to possibly identify the unknown IP address. You are looking for ARP packets, generally, and the ones that are ARP requests or gratuitous are particularly useful for this, and they are sent as layer 2 broadcast so you will see them, no matter the IP range.
The issue with the Wireshark method is that it requires the unknown device to send these packets; many do: at startup for IP conflict detection and then sometimes periodically for continued probing. However, not all devices do this.
Sometimes you might get lucky and the device tries to discover it's default gateway, or maybe a DNS server, or even an NTP server, so will issue an ARP request for those IPs. These packets will provide information that you need too.
This assumes the device has a static IP. If it is configured for DHCP or BOOTP, that's a big help. Wireshark will show you those requests - in which case then setup a suitable server to provide the IP and then you would know what it is.
More advanced devices like routers and managed switches often send discovery packets (such as Cisco Discovery Protocol, or CDP, and others) that may contain the IP address in the data that is broadcast/multicast on the wire so inspection of the data in these packets sometimes yield useful information.
Your best chance with this method is to plug the unknown device and your test pc into a switch - just these - and power cycle the unknown device.
IP scanners are great - I personally use nmap or zenmap - but I only use if I know the subnet. I suppose it's possible to scan all possible IP address ranges but I suspect that may take hours/days/weeks? Would never consider it so don't know how long. If you got this route, suggest you assume the unknown device has a private IP address consistent with RFC 1918. This assumption will cut your search space down significantly. Of course it may be an incorrect assumption; you have to evaluate how valid it might be. It's where I would start 100% of the time, unless the device is directly attached to the Internet, and it's possible that the enterprise has been allocated real IPs.