Basically, I'm wondering if the problem from Forward SSH traffic through a middle machine can be solved using PuTTY. I gather I could start one PuTTY session to create an SSH tunnel to the first machine, then another session to use the tunnel to connect to the second machine (or just use ssh manually from the first machine), but I'd rather have a 'one click' solution.
The most elegant solution I can think of is automating the PuTTY sessions from a BAT file. Basically it would just be two lines launching PuTTY with command line options. Launching the BAT file would then be 'one click.'