Given that this is a thread that has been idle for 10 years, I'm guessing "NO" on the answer.
I don't think it will be easy, but here is an article about using some sort of API that might give you a lead. It mentions manual tunnel setup but also suggests a more programmed approach.
When you open a tunnel, you can choose the quick setup or the manual setup method for opening a tunnel into the remote device. This tutorial shows how to open a tunnel using the manual setup method and configure and start the local proxy to connect to the remote device.
docs.aws.amazon.com
You can continue looking for this answer by doing a web search on "ssh tunnel vba" or "ssh tunnel without putty"
I found this link which MIGHT help. Not entirely sure as it may involve a 3rd-party library.
Recently i faced a situation where I had to connect to MySQL server via VBA to extract the data for reporting. (Sounds simple .. Think agai...
unlimitedexcel.blogspot.com
This is an EXCEL solution:
Hello, I know that directly connecting to a MySQL database on internet is not a good idea, but if we use a SSH Tunnel (like Putty or Chilkat ActiveX) would this be a secure solution? So that we don't need to rewrite the whole legacy app codded in vb6 to use webservices? Do you have any...
www.vbforums.com
Somewhere in there you might find a nugget you can keep.