Rich,
I operate an Internet remote control station that is very similar to what you are using: K3/10, homebrew 1KW solid state amplifier, Teamviewer, and Skype. I operate FT8. I have used it with the WSJT software running at my operating position and connecting the audio via Skype, and I have also done it with the WSJT software running at the station location and using Teamviewer. I have very slow DSL Internet, only about 300K upload. With this limitation I find it better to use WSJT from my operating position and Skype for the audio. I connect CAT using VSPE TCP/IP server. I also use this for a remote HDSDR panadapter and a PigKnob which I use for SSB and CW.
73,
Don
K9AQ