This is a great workaround and indeed a CUFP.

I call it a workaround and not a solution because there are two much better ways to do it.

OpenSSH is one. You can get command-line ssh (including OpenSSH) for non-cygwin Windows. Plink, a tool from the PuTTY toolset, is one of my favorites.

Centralized server administration, while a drastic step, should be considered for this many machines. Having your credentials served from a directory or database and your home directory served from a network location (via for example NFS) could allow you to have one password and one ssh private key. Short of networked home directories, rsync or similar in conjunction with the very type of multi-box script you're writing could keep your private keys synced. Unfortunately, this decision typically involves much more than just the person it would help the most, and it involves time and cost estimates for up-front infrastructure work vs. your ongoing costs.

As an aside, I use both Cygwin and some native Windows ports of Unixish utils. http://gnuwin32.sourceforge.net/ is one source of these, and http://unxutils.sourceforge.net/ is another. I don't think either package includes ssh, but it's nice to have these for the odd one-or-two command task that doesn't need Cygwin. It's also much easier to carry these around to other systems than all of Cygwin. This type of package sure beats when I wrote rm and ls as DOS batch files.