Import ~/.ssh/config into Putty
I must also apologize, I hate when people answer "Don't do what you asked, use this other software instead". Hope you don't mind. https://cygwin.com/install.html
If you're familiar with ssh on linux, I might recommend not migrating to PuTTy.
I have fully abandoned PuTTy on my windows workstation and instead live in cygwin + tmux + openssh.
Just copy your .ssh/config to your home directory in Cygwin and you'll be good to go.
My suggestion does assume that you have permissions to run the cygwin-setup.exe