Try using PortaBase at http://portabase.sourceforge.net/
Portabase is great, but it's not relational (from the original post, though, it really doesn't sound like relational is needed).
That said, there are some relational DBs that run on both the Zaurus as well as Windows, aside from MySQL. There's picoSQL - full server and client (Zaurus, Win, Linux), and a PostgreSQL client for Zaurus, server on Windows and Linux, HSQLDB client that connect to various types of databases on the server-side. I also understand that Daffodil DB runs on both the Zaurus and Windows, alothough I have no experience with it.
But really, unless you want to actually do SQL and have the overhead of an RDB, or have special datatype requirements, why not just use Portabase? It stores all your data neatly on several different platforms.
R.
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