The commercial products Tunnelier and SecureCRT can do this for shell windows and their bundled sftp clients. Didn't check if they can support third-party tools

The commercial products Tunnelier and SecureCRT can do this for shell windows and their bundled sftp clients. Didn't check if they can support third-party tools like git. But even for shells, I went back to PuTTY anyway -- It came down to cost + time setting up on new machines vs. using PuTTY's "Duplicate Session" feature with ssh keys loaded into Pageant. Since then I've moved on to using a persistent X11 VNC session over a plink tunnel :)