Well that sounds like something I have no idea what to do about.
I have 1 Homegroup as Home Network with file sharing enabled, it contains both my Wireless Network Connection and Hamachi. (Listed first)
My Network Adapters as shown in order on Device Manager:
Broadcom 802.11n Network Adapter
Broadcom Netlink (TM) Gigabit Ethernet
Hamachi Network Interface
That's all. Is the LAN adapter you're talking about the second one?
I can disable it at no loss, I don't use it. Trying that now while messing with IP/port settings on both the server and Hamachi.