Microsoft and Skype appear to have made a final decision to totally remove any fast peer-to-peer file transfers, as of at least version 6.18, released in August, 2014.
Your only option for FAST LAN file transfers is to downgrade to a previous version, before 6.18.
Version 6.14 appeared to be more stable than 6.16; but I need to confirm. Further, there are no longer ANY previous versions of Skype available from Microsoft/Skype, and you must obtain them from places like the WayBack Machine.
Advice If Downgrading:
If you downgrade your Skype version, this will likely be temporary. I predict that all updates will become forced very soon, as they've stated that all auto-updates will mandatory with Windows 10. This also will mean they will permanently break any previous versions of Skype. As of today, March 31, 2015, Skype is now upgraded automatically through Windows update, KB2876229. Your only option for disabling this is to right click in Windows Update, and choose HIDE. But, even this may be temporary, since a future update may “unhide” that KB, or issue a new one, just as they did with the Windows 8.0-8.1 forced upgrade. This will still not disable updates from being requested inside versions 6.18-6.22, for which you must also turn off the “Skype update service.”
For more information, see Skype's official forum posts:
GET version 6.14 (which should be fast and that has the good UI)
GET version 6.21.0.104
This has the last good UI, but slow LAN file transfers.
NOTE: 6.21.81.104 has the BAD "blue bubble messages" UI that wastes space.
Here are some tested links: VERIFY the MD-5:
Skype 6.21.0.104 (EXE version) [web.archive.org = from Skype]
File size= 36,039,776
MD-5= 6082D256DCDCD068F76B677DB8ED1181
Skype 6.21.0.104 (MSI version) [web.archive.org = from Skype]
File size= 26,951,680
MD-5= E5C8C6127AA2B57CBA3116C523A6D1C9
Allow direct connection to your contacts only
option under Options->Advanced->Connection