Is there a method to determine whether a host (on your LAN) is on WiFi vs Ethernet using nmap or any other tool? I am OK with fuzzy guesses as well.
tl;dr No, there is none
Long answer:
There is no way to find out what kind of connection other PC on your network is using(without physically accessing it ofc).
Those things are abstracted on network. You can sniff traffic on transport layer by Wireshark and see there is no data on interfaces being transported.
An option:
You can learn a physical network interface vendor by sniffing traffic.
Wireshark can guess those, because vendors have their own MAC address prefixes. And if it's some company which is making wireless interfaces only, you can hit a jackpot. It's not even close to being a bulletproof method though.
Nmap may be used to look for open ports. There might be a chance that you can deduce which software server is running by getting info on ports, but I can hardly imagine you will find anything wlan/eth specific.