Thank you for the quick and highly useful responses.
I'm using the "new" version. I will try to download the old one and use that.
This is what I did (a combination of things):
1. I had already deleted the shortcuts in startup but I double checked and nothing except onenote clipper which I use.
2. Check the background app settings. Woah. I disabled everything. Most I didn't know were even on.
3. Run msconfig. Omg. It's another hidden interface and black hole. But no mention of skype anywhere. I'm thinking it's tightly integrated into office and there's another setting somewhere to disable it?
4. Get the sysinternals. Muchas gracias! Another useful, yet carefully hidden-away tool.
Searching on Everything tab for "skype":
HKLM\Software\Wow6432Node\Microsoft\Windows\CurrentVersion\Explorer\Browser Helper Objects 5/14/18 13:26
Lync Browser Helper Skype for Business Microsoft Corporation c:\program files\microsoft office\root\vfs\programfilesx86\microsoft office\office16\ochelper.dll 4/2/18 17:17
HKLM\Software\Wow6432Node\Microsoft\Internet Explorer\Extensions 5/14/18 13:26
Lync Click to Call Skype for Business Microsoft Corporation c:\program files\microsoft office\root\vfs\programfilesx86\microsoft office\office16\ochelper.dll 4/2/18 17:17
I remember having 2 skypes installed, maybe 3? I can't recall now. So Lync is now Skype? I also have Office... I'm not messing with Office.
I don't see skype at all in control panel btw. It is under the new Settings->Apps. Side question: why are there 2 control panels and the list of what's installed different on each one.
I uninstalled skype for business because of some other issue which I don't remember now. I guess it didn't completely uninstall AND my locked-down background app setting are causing skype to crash "the new skype".
It might be my laptop though - I have also run thinkvantage system update which also has its own update lists and host of issues.
I sincerely appreciate your help.
I'll post back if I figure out what's going on.