Are you willing to at least connect the device to the internet for initial configuration (which will include the near-mandatory 'apply updates' phase)? Here's what should work -
Set up two wifi networks within your home. Most people have an old wifi device that they've superseded. Your primary home wifi / router device will be the internet gateway, with the second, older device just a wifi access point connected to your home network. Set up the second access point with a different SSID and password, so that none of your other devices will 'see' it. At this point, both wifi access points will have internet access. Now, set up your 'smart plug' and make sure it connects to the 'second' wifi access point. Connect your phone to this second wifi access point also. You should now be able to control the plug from the phone.
Once you see this working, disconnect the second wifi access point from the main network. This will now be a 'standalone' wifi network inside your home, and only the plug will be using it. You'll have to switch your phone between the two wifi networks if you want your phone to have wifi internet access while at home, but if you don't mind, then let the phone just use cellular to get to the internet.
I have a smart plug from Wemo (a belkin brand) that works in this manner - it does not care about internet access for daily use.